Okay, so while that's coming up. Yeah, I'm starting with recording any questions any questions Okay, so we're looking at these four areas of compatibility. So From those a few who are single any questions Any questions any fears, you know, like like one question That I thought you might have okay, just correct me if I'm wrong. Okay, what if you know, I look at these Characters, I mean these areas of compatibility and then what if I harsh I mean judge very harshly and Then I let go of that opportunity Maybe God is sending that person Into my life and then You know anybody thinking like that Okay, you have a question or your Anita But I have a question actually you have a question. Okay. Okay. Go for it. I mean, I have that fear as well I mean in that area of compatibility in life's calling. Yeah, I mean, I Know I have a calling to be here in village. Actually, I'm serving here in village So I have that fear if I'll get a person who is from a city and I Mean, I don't know how to react to that how to prepare for that. I don't know Yeah, so the thing is to Specifically in your case let's say Yeah The thing is to just you know, your fear is okay. What if I don't you know, this is This is your do you feel that okay? God is calling you to this But are you very sure that God is calling you in a like to a rural kind of a setting? Yeah, okay, so Okay, okay.  You know thing that They will also have a similar passion a similar vision at least So, you know, let me So I just start praying towards that and And also look for those, you know, when you when you're maybe even a proposal comes right you you can Like I'm sure there'll be a time for interaction and questions. So this can be one of the questions, you know, we can share saying I mean not like a You know, I share very graciously saying, okay This is what God has called me and I feel that this is this is something that is very big very important in my life And what do you what do you think? right, so It's good to get that Get that clarity from the other person also the person says, yeah Well, there could be things maybe there there could be ways that it could be accommodated also, you know Let's say the person is in a urban setting and then the person feels that okay. Can we do it this way? You know, there could be ways where can we can I come with you on weekends and you know, can we do it this way? Um, I don't know if that's that's something that's possible So that could be you know one The discussion could go that way saying that okay, this is an option I also have this passion but because of you know, this season of life Uh, and uh, since we are working this way and Could we do it this way? You know, could we go there on weekends? Could we go there? like do some Mission kind of a trips on vacations. Can we can we do that? right Maybe that's that's something for you to pray about and ask the lord as well Yeah, okay Okay Okay, one question from the married couples like those of you are married um Well, the married couples are silent Married folks are silent married couples married folks are silent um I don't know what to make of that But really, you know, um, if we you know as And when there's compatibility, it's amazing, right? It's like Yeah, it's fine. Uh, which is moving forward a lot of progress We're literally cruising if there's In incompatibility You know in these areas and that's areas for us to work on Right. We are in the covenant. We have uh, we are committed to one another And this is a area for us to work on All right, we are works in progress is area for us to work on Yeah, and um, yeah, that should be our Our posture, right towards these four areas Okay, okay, so we looked at um, like some questions to consider, you know, like signs signs of immaturity uh, is the other person Preparing or is open to preparing? Or is there a lack of preparation towards marriage? Are there any signs of character weaknesses? Okay So, uh, so don't get into a you know, we shouldn't get into a marriage You know marriage covenant saying okay, I'll change the person I'll change the person with my love and understanding and everything You know, once a person gets to know me he will change she will change Wow, that's uh, that's a and that's a very very uh, I don't know You know, that's self-deception We Yeah, the person may change person may not change but the change comes when person when that person decides to change It's it's not like, you know, you and I cannot change force another person to change, right? Our lasting change transformation comes when the person, you know, uh decides and then there is also, you know the The work of the spirit holy spirit in them and then there's transformation is a lasting change Right. Okay. Let's look at a few more. Uh, you know areas or red flags to consider signs of parental control. Okay, so it means that um Are the parents You know involved too much Right controlling everything Every decision uh of that person Okay, the person says, okay, you know, uh, I think we'll uh I'd like to do this and the person and the and the parents Uh Of that potential spouse right parents. Um, interference. You're okay. No, no, no, you cannot or No, you should not and and there's a lot of Control happening there. You know the control could happen because you know, that's how they've lived their lives, right? Um, you know as parents and they've brought up the child. So they obviously, you know, why do parents do that? It's because they want the best for the child, right? So we should consider that you know, they they don't want the child to um To undergo any pain to make any bad choices And there's a lot of involvement while we you know, while they bring up the child. So the but what happens is that Uh, you know as people grow Uh, parents also need to kind of let go and give that independence Right independence and making choices independence and living their lives and and not really force not really live You know, I should not live my life through my child you know, um And uh, say okay, I I did not get to do it when I was uh, you know when I was growing up Now there are these options, you know, I since I didn't do it now. I want my child to do it Right. I didn't become a doctor now. I want my Son or daughter to be become a doctor You know, that's that's not correct, right? We are imposing our life upon Whatever god's call might be for that person, you know It could be something totally different, but we are imposing and saying this is how it should be Okay, so similarly what happens is parents Uh, do not let go Of that or do not give that independence to their son or daughter When they move into a season where it's a different season where it's marriage Right where it's um, they they are married and all other relationships Take second or comes second Um, and this takes precedent which means that they are A couple and they are going to be making some choices for their lives For the for them together as a as a as a couple and as a family. So now as parents we can Well, parents can advise parents can guide of course from their wealth of experience and having walked with god and can give godly counsel but It stops there, you know, I cannot enforce My will and wishes that I'll be interfering in the marriage Right, so is there parental control? Okay, uh, that's very important. So if they're going to say no no my son will only do this Oh, wow Okay, we need to you know, take note of that. Okay, so Um, I'm not sure if that happens in every culture, you know, I I see, you know Like georgia abubakar and lubega And also, you know, like success is in wells. Isaac was here a little while ago So, you know, we we know that, you know, we're from different Cultures different nations and maybe even within our own nation like zealotoli from the way up north and And all of us, you know, in different places. So we, you know, our cultures might be different and So it may not directly apply, you know, this thing of parental control, but But that's a sign to watch out for, you know So I'm just we're just looking into that and the other thing could also be parental dependence Right. Um, hey, shall we, you know, shall we go here? Let me ask my parents, you know, so Hey, but, you know, you're you're an adult now You know, I just want to ask my parents just in case, you know, I want to make sure that they are okay Um, you know, that now that's again Going to be a problem if there's a lot of dependence and attachment Uh, to the parents now again, we need to honor our parents We need to respect our parents just because we are married doesn't mean that we are totally cut away. Okay, but We need to understand that The person whom we are married to or considering marriage Considering being married to should not be dependent on the parents for each and everything, you know Emotional dependence or maybe financial dependence or maybe, you know, other things If you're going to be totally dependent for each and everything, then now that's going to create A problem, right? That means that the person maybe Is not emotionally strong enough emotionally mature to handle Marriage or get into marriage Okay now uh One more. Okay, so While we are considering all this and saying, okay, now I need to make a decision It's so we can obviously, uh, you know, I'm talking to single people you can definitely get the council of parents Right. Sometimes we think, oh, what do they know? Right. What do they know? They don't know about my life times have changed and you know, um But the thing is they can give a perspective about that person they can read Uh, you know that person whom we are considering and then they can look at certain aspects certain characteristics Of that person that we we might totally miss out completely miss out Okay, completely get blindsided by either by our emotions or by you know, whatever We didn't even look at it, but then parents can do that or spiritual mentors You know some elders they can give that perspective.  So do they did they observe anything that was off? Did they observe anything that was uh, that could be a potential problem? Right. Um, so they could do that. Okay. So, you know, many times when you look at these questions, you know It might seem like are we overthinking this, you know, our parents didn't they didn't go through all this Uh, but I want to remind us that you know, the the society that we are living in the times that we are living in Is is way way complex, right? And also there's a lot of influence From media that we have been exposed to that, you know, that generation or the two generations earlier Did not have, you know, all that they grew up in was pretty much, you know This is what the friend circle is what is happening and that was it now there's so much of Uh, so much of so many voices You know, they're dictating stating, uh, this is how, you know, you keep your expectation should be Okay, like perfect bodies and perfect, uh, you know, perfect vacations and perfect pictures and perfect places and everybody's like Having that expectation. Oh, if it's if it's a marriage, it should be like this. If it's something out of it That is not Okay, so so there's a lot of you know, this kind of information, um coming at us And so we it's important and also different kinds of definitions definition of marriage definition of Husband definition of how the wife should be. So it's it's important that we look into the world and not lose that biblical perspective And and and look into all these aspects and prepare oneself Right for marriage. So that's why we are looking into it. It's not a question of overthinking or complicating things But really, you know, looking at all these different aspects and of being prepared for marriage, okay okay, so so the thing is If you're so we looked at all these red flags, um, you know these signals these signs to watch out for um And also, you know for us to reflect If you're a single person to reflect and say, okay, what would your what would you like? Yeah, the person that you're considering to be a spouse, what would you Like that person to be right What are some qualities that you are looking for? And prayfully consider that, you know The thing is it's it's not like, uh, okay god, what do you want? God is looking at you saying and saying, you know, what is on your heart? Right.  That's not my desire. He's given you Right. He's given us The power of choice and also certain, you know, the way he's created us and designed as we have certain likes and dislikes So what are those characteristics that you like in a person? right To be your life partner. So It's good to list that It so in listing that, you know, you get an understanding. Okay Is this is this something that really matters? Is this something that's important? Now, maybe, you know, we've never thought on those lines Right. We've never thought. Okay. I want my life partner to be like this Maybe we've never thought you know, we've been thinking about all other things and Maybe this whole thing of marriage and everything was just in the back burner And suddenly we are studying about marriage and family in valuable college and maybe we never even thought of those things Right. So it's good to think. Okay. If I want my person to be, you know, a life partner Um, if I'm considering someone, you know, what are those characteristics? Okay. What are those qualities? um question number two You know, what are my expectations of marriage? What do I expect marriage to be? I remember these questions, you know, I found it difficult to answer because it was like, um I'd never thought of it Right. So when we had when I had my, um, I went through this marriage preparation time Uh, I found it. Okay. First time I'm encountering these questions. So I really had to think And uh, okay, what is it? I really need to get in touch with myself, you know, ask myself, okay, what is it that you want? Um, okay, what are your expectations? What kind of a home and family would you like to, you know, Build or come home to right? Um being practical and realistic now the thing is when we answer these questions we can be get very we can get very very idealistic uh, and So things to be realistic, you know, um, this is how we practically Okay, another question. What traits and qualities can I bring Into the marriage very important right, what are those traits? What are those qualities that? Me as a person me as a spouse, what what is it that I can bring? Okay, uh into the marriage so Well, I can bring stability. I can bring provision provide um, I can bring, you know, uh, maybe joy and laughter and I can be understanding I can bring patience. Uh, these are things that I've been blessed with and you know to think on those lines What can I bring into the marriage for the benefit of my spouse? Not always thinking about what that person can bring into my life Right to think what what can I bring into uh marriage? Okay, another question. How can I help towards building my marriage and building a home? Um, how can I how can I help towards that? Okay, no, these are my expectations This is how I want the marriage to be. This is what I want. I want to have the I want the home to be Good expectations practical expectations real expectations, right fine now What can I do? What is what is my contribution towards it? Like what can I bring? How can I build That or Satisfy that expectation. What can I bring? Okay? So some of these questions it'll be good if We can take some time if you can take some time to answer. Okay for those of us who are married It'll be like a reflection. Okay. Now I'm married Now I want My marriage to be like this Right um, and my expectation is lying home My family It should be in this way. So What can I do? What can I bring? Okay, so those are questions that um That we can answer if if for those of us who are married Okay, let me look I'm going to look I'm going to look at a very important A question which is Let's say You know, there is a proposal that came Um, I'm I'm you know, I'm talking when I say proposal, of course For an Indian in an Indian context, it would make sense, right? You know, or maybe you know, there's someone who who who was interested And who said that they were interested in getting married and but you for whatever reason Okay, uh, you just said no okay so You know, maybe there's a question in your mind saying, okay, I said no to that proposal. I said no to that person now I didn't consider God. I didn't consider any of these things and I just said no Now do I have to remain single all my life? You know, maybe that was the person that God brought And I said no and therefore since I said no Uh, do I have to remain single all my life because I said no to that person God brought okay, so in other words, you know, is there Just one person in my life one person that God Wants me to marry Of course, God wants me to marry one But if I miss out on that If I miss the bus Is there another bus that is coming my way that I can reach the same destination? Right, so that's the that's the question, you know, so Let's try and answer that okay, and we can look at Genesis 24 This whole instance normally, you know in engagements And and also weddings normally engagements, you know, when there's a formal engagement people normally share from this Genesis 24 about Isaac and Rebecca and how I you know, Abraham sent servant to find An ideal bride for his for his son, so we see that right? So let's look at Genesis 24 And versus one two in your notes. You have that whole, um, you know the whole Scripture portion there. It's in the good news version, but uh, yeah, I just want to Let's let's read that. Okay Now Abraham was very old and the Lord has had blessed him in everything he did He said to his oldest servant who was in charge of all that he had place your hand between my thighs and make a valve That's the you know, customary time of What do you call a symbolic way of saying okay making a vow of those times So I want to I want you to make a vow in the name of the Lord The God of heaven and earth that you will not choose a wife for my son From the people here in canon, so Abraham did not want any of the canonites Um, you know to be potential bride for his son So said you might go back to the country where I was born and get a wife for my son Isaac from among my relatives, but the servant asked what if The young woman will not leave home to come with me to this land Shall I send your son back to the land where you came from? Abraham answered make sure that you do not Send my son back there The Lord the God of heaven brought me from the home of my father and from the land of my relatives And he solemnly promised me that he would give this land to my descendants He will send his angel before you so that you can get a wife there for my son If the young woman is not willing to come with you You will be free from this promise But you must not under any circumstances take my son back there So the servant Put his hand between the thighs of Abraham his master and made a vow to do what Abraham had asked The servant who was in charge of Abraham's property took ten of his master's camels and went to the city Where may her had lived in northern Mesopotamia When he arrived he made the camels kneel down at the well outside the city It was late afternoon the time when women came to get water He prayed Lord God of my father master Abraham Give me success today and keep your promise to my master Here I am at the well where the young women of the city will be coming to get water I will say to one of them Please lower your jar and let me have a drink if she says drink and I will also bring water for your camels May she be the one that you have chosen for your servant Isaac If this happens, I will know that you have kept your promise to my master Before he had finished praying Rebecca arrived and we know you know all that happened, right? so so he's on this important journey and he's He's there to get a bride for a choose a bride for his master's son Isaac okay, so if we look at verse Five, you know, he asks a very important question to Abraham. So he asks about you know, what if He's asked what if We this situation is not ideal Okay, what if okay, I go there You're sending me. I need to find this person. Okay. I narrow down to the one Okay, but what if she does not agree? What if she does not say yes to this proposal? Right And and then Can he says, you know, can I send your son back to the land so that he can find someone there? Okay, so Abraham says no don't send my son and he says, you know, if You're free from this promise Okay, if this does not happen So there was we're looking at verse eight, right if the young woman is not willing Okay, so if she's if she doesn't say yes to this proposal You know, you're free from this promise. So they're looking at that option where it's not like uh Well, there is this one And if we if that person says no for whatever reason then that is it that's the end of the matter Right. So there is this possibility that Rebecca could have said no She could have said no right Because why? She's a human She's been given free will She has the ability to make a choice make a decision And she has likes and dislikes fears expectations all that She could have very well said no And there is that possibility Of Rebecca saying no Okay but he in head down we prayed and You know, it was 15. I think it is so where it says that Before he finished speaking off in his spring Rebecca was there and says that Uh, then the whole thing like that we have they have that conversation was 17 And and we know what happens like it's exactly like he prayed. So now, um Okay, he he wanted to He wanted the Lord's guidance Okay so that's the thing that we notice here he and in a and We know that progressive revelation, you know, which is studying in You know, homiletics about hermeneutics. Sorry the fact that okay according to what he knew according to what his understanding Of God or a relationship with God was he he said, okay God This is how I will know That this is the girl Okay, so we don't have to use the same yardstick. Okay, she'll be wearing this or he'll be wearing this He'll be you know, we don't have to do that. Right. We have the word of God for You know the kind of person that we have the word of God We which which describes the desires of God the will of God, etc. And we have also God's spirit to lead us oops Sorry to lead us and to to guide us to make that choice. Okay, so we we We have the indwelling presence of the Holy Spirit as believers. Okay, so so he Does this he says, okay, if if the if the girl You know gives me water and gives the camels also water then I will know that this is the girl Okay, and which she which he does. Okay now the thing is uh Okay, he dependent on God for guidance and the second thing is he gives the choice to the girl and to the family Okay, so that is something that we see here Right So after the introductions said um He said blessed be verse 27 and he said Blessed be the lord god of his Of my master, Abraham was not forsaken mercy and truth as for me being on my way The lord led me to the house of my master's brethren uh, and then she goes and she uh informs the family and uh verse 30 um It was 30 if you read and it came to pass when he when he saw the nose ring and the bracelets on his sister's wrist And he heard the words of his sister rebecca saying thus the man spoke to me That he went to the man and they uh, you know stood by the camels and said come Oh, blessed of the lord. Why do you stand outside and so on so she basically you know is the In the conversation and in the you know all those things that he had given the choice for rebecca And he's given the choice for rebecca's family to decide Okay, so that is that's the second thing that we see here. Okay, so Uh, it is not as if he said, okay, I've seen the sign This is the sign that I asked for Um, god has led me. This is the girl And he did not say okay god has promised god has uh this thing. So therefore You need to agree no matter what you need to agree. This is the will of god This is the promise of god God has guided and so you need to You need to agree You know, so he did not use any kind of manipulation spiritual manipulation um And in any way he did not You know, he did not use that To force them to come to a decision Right, we see that also just left the choice Right And and this was the response, you know, they said Um, uh, laban and bethwell answered since this matter comes from the lord. It is not for us um To make a decision Okay, um, so that is their response if you look at verse 49 says now if you intend to fulfill your Responsibility towards my master and treat him fairly, please tell me if not Say so and I will decide what to do Okay, so he did not impose on them Because he had seen very clearly. This is what happened. He prayed he asked god and this is what god led So the sign is very clear, but he yet he gave the choice to them. Okay, so these are lessons for us to learn Lessons for us to you know apply. Okay So we know that Rebecca had to make a choice and rebecca made a choice. Okay, let's look at the Verse 57 Okay, they answered Let's call her and find out what she has to say So they are called rebecca and asked do you want to go with this man? Okay, yes, she answered so they let rebecca and her old family Servant go with abraham's servant and his man Yeah, so a big rebecca very clearly she Made a decision she made a choice and she went Okay, so so the question is okay if rebecca had said no despite all that leading and guidance Was that the end of End of the road for isek Okay, so that's the question right? Is that the end of the road for isek? Yeah, does isek have to remain single. What do you think? Anyone, what do you think? Okay, let me ask a few people Okay, liya lama What do you think? Okay zealotoli Okay, I know he has a free will to choose. Okay, so isek has a free will So he can choose So so the thing is this, you know that No matter what You know how we come You know arrive at that choice and of course we need to be led by god. We need to Um, you know understand all this and have the right reason For getting married and and our hate expectation, etc. You know Well, we need to understand that Well, god will lead us god will guide us And it's ultimately You know finally we have to make a choice The other person has to make a choice And if we choose differently Okay, we say okay god, you know I'm saying no Maybe it was fear. Maybe it was Whatever, you know, we maybe it was a mistake You made it That's not the end of Our life or that's not the end of the story right Well God would Lead us to another person. But the important thing is this you know when we make a decision We will have to work at Building a marriage We wouldn't need to invest. We would need to do our bit We would need to do our bit and preparing and doing a bit in in that marriage Okay, so Even if the person, okay, even if there's let's say in this case, like, um, like God led we we we obeyed Ideal situation, right? We are we're saying yes. The person also said yes In such a marriage also One has to prepare one has to work at it Okay, now that's the truth. That's reality Okay The reason being this whatever we studied, you know People are different people come from different backgrounds different expectations, etc So one has to work at making the marriage work In building and making it great. One has to do that um So god leads us So the conclusion is that god leads us to the well, he will lead us to the most suitable person. He will lead us To you know, he'll give us those options But ultimately, you know, we pray prayerfully We pray them, you know for the heart of god for the mind of god and then we make a choice And since it involves the will of two people here Right, uh, it involves the will of two people here. So that does not mean that You know god has only one person And if you miss that That's the end Okay, so I know, you know, that's a school of thought right God has because we we say, you know, god has a person prepared for you And even as you are being prepared, you know, god is preparing that person And uh, and then many times we put ourselves under a lot of pressure.  No That's not the end Understand that The choice you make, you know, you need to work at the marriage, you know, that's the bigger picture Okay, so making the choice is important Definitely making the right choice, you know, leaning on god leaning on, you know, all that we saw, you know, getting godly counsel very important but The most important thing is that you need to work at a work in Work at making the marriage great. Okay, that's your responsibility. Okay, then the other thing that we need to Also understand is um that That god honors our decision in marriage Okay, so meaning that you've come you've uh, you know, you've made a decision And you're you decided to get married and you do so You make your vows you make uh to covenant one with one another god honors that Right, and the thing is this, you know, you're going ahead and and you are You know making covenant with god as witness So god honors that right, so So we need to honor Uh our vows our covenant that we have made In the presence of god, okay So it's not just about Finding the right person It's not just about being the right person right it's uh, it's about uh working daily day-to-day basis And in walking through the vows that we have made The covenant that we have made Right, so while it's important to find while it's important to be right person, you know It is important to work out or walk out the covenant meaning practically live out The covenant that we have made Each and every day of our lives in marriage. Okay, so that's the bigger picture Right, that's the important thing No, that's a more important thing. I would say right. Okay. Any questions here Any doubts here? um Yeah, okay, jeffina Okay, jeffina is right here. She put her hand Yeah, jeffina you want to put on the chat or you want to ask? Okay Yeah Okay Yeah, so good question. So In the case of adam and eve, you know, there are no other choices It was just adam and eve, right? so There's no evangel in to consider So there was you know, it was just adam and eve. Okay, so that was uh, so it's things were simple and that's the thing so Like while we while we say, you know, I know in a manner of speaking we say, okay I found my missing rib Right in the in the in my in the spouse who my matter to I found my missing there about a fine You know something in a manner of speaking we say that because it's uh, you know, he's a he's a right person. We found and we So, um, we use that well Scripturally, uh, there's not a validity, you know to that I think as a manner of speaking it's we can use it There's nothing wrong in it. But um, but when we look at it, uh, we look at it scripturally. We see that well Uh, you know, we look at all these possibilities. No like what if What if the person did not make a choice, uh, you know, despite everything being right? What if the person just You know, um, show someone else, you know, so is that the missing rib, you know So all these things so, um, so like I would say, you know, yes It's fine. I you know, it's it's it's nice when you when you meet the right person Then you make the right choice and then I mean you just say You know, uh, that's that's a missing rib. I found what was missing, you know, that person Uh fills that that place in my life and and that's that's great But I don't think we can go beyond that. I always should go beyond that Yeah, correct Okay, any other question, um Any other question Yeah, okay, Anita, you know Yeah Many people ask me this What is the right time to Look that choice like right age to make that choice that that person is for you or He's the one or she's the one Okay, so what what is the right time to get married? Is that their question? Right age to get married Right age or right, uh, right time to make the decision of That choice, I mean, yeah Yeah, what is the thing so, uh, I mean we can look at it, you know, several ways, you know, like we we look at these areas of compatibility so spiritually And also the seven areas that we looked at, you know, so to see You know, am I Developed in these areas, you know, am I able am I ready to handle this? Uh response because sometimes people are not ready They're not ready and they have a terrible time You know, uh, just and it really breaks them people are not ready. So, um, am I ready financially? Am I ready emotionally? Am I ready relationally? Am I ready?  So that's the thing. That's why we have that age.  Okay beyond this age you get legal age for marriage Right 21 or for the mail and and so on. So, um, so Are we developing all these ways? Right. So that's the that's the thing, right? Um, but beyond that, you know, for a believer I think it makes sense. You know, is the person Ready person Spiritually also is the person ready for a commitment Is the person ready for for the responsibility? It's it's a responsibility. It's a privilege It's a responsibility. It's a it's a commitment So is the person ready in all these ways is the person mature And ready for this So some of these readiness could be just a practical aspect of it. Hey, do I have enough money to run a household? You know, it seems like It seems great to know we didn't have any money, but we still got married. But then there's a lot of stress Like so the practical thing is okay. Do I have a work? Do I have a job? And I employed to take care of my bills not to take care of Running a household. Um, so those kind of very practical, uh questions also to consider and say, okay If I'm ready then, um, then I can go ahead and do it Thank you Okay, so said can is a question is okay. What are your views on inter-religious marriage intercast marriage from the biblical perspective? Bible is very clear About inter-religious in the sense you're coming from a different world view. Okay Um, so it's it when I say when you say inter-religious, it's it's more about okay Am I a believer or not a believer? All right, uh, that's the thing. I might have been born in a different faith But am I a believer or not a believer? I think that's the very important question. So Uh, Bible is very clear. Uh, do not be Uh unequally yoked to an unbeliever. So that's I think that covers everything Right, uh, so that's the thing and then when it comes to inter-cast marriage Uh, I think caste is a man made issue Right is a man made problem. Uh, and uh, so the bible does not say anything about that Right, so so the bible gives that broad thing. Do not be unequally yoked to an unbeliever. So if it's a believer Then yes, you can go ahead But we are also looking at these aspects, right today compatibility on all these various fronts So so that is a biblical perspective. I said, you know Okay, okay. So, uh, 1050 will stop here and then we'll take a break Um And continue next class. Okay. Thank you. You got this


The abstract text has been simplified into full sentences. The first sentence summarizes the main point of the abstract, while the second sentence introduces the topic of the paper. The third sentence explains how the paper was conducted, and the fourth sentence introduces the results of the paper. The fifth sentence discusses the implications of the paper's findings. The sixth sentence introduces another important aspect of the paper, namely its potential use in human-machine interactions. Finally, the seventh sentence concludes the summary. This article was authored by Kuimpeng Chen, Jinyu Zhou, Miao Miao, and others.


They say the only constant in life is change, changing trends, technologies, market demands, a changing climate. All these changes impact the food we eat, and the global food system that provides it, including the livestock sector. Across the planet, around 1 billion people rely on livestock for their livelihood. They must be able to adapt to their changing environment. And so must their animals. How can we ensure livestock are more resilient in a changing world? For FAO, a key solution is the diversity of animal genetic resources, and the fair exchange and movement of these resources across the world. Today, the genetic diversity of livestock is distributed, across 40 species, in separate populations within these species called breeds, and among the animals within these breeds. But this diversity is under threat. Out of 8,900 breeds registered in FAO's Domestic Animal Diversity Information System, dad is, 2,400 are at risk of extinction, while 600 are already extinct. These numbers could be even higher, as the risk status of more than 50% of breeds is currently unknown. The genetic diversity of livestock breeds and species provides the raw material for evolution. If managed sustainably, this diversity can be used to increase production and allow livestock to adapt to challenges such as climate change, emerging diseases, and pressure on feed and water resources. But for this to happen, countries need to strengthen their efforts to implement the global plan of action for animal genetic resources. This is an internationally agreed framework that describes measures related to breed characterization and monitoring, and their sustainable use, development and conservation, as well as actions related to policies, institutions and capacity building. FAO's Intergovernmental Technical Working Group on Animal Genetic Resources for Food and Agriculture is working to achieve this. The working group was established in 1997 by FAO's Commission on Genetic Resources for Food and Agriculture. The commission is a permanent forum where 178 member countries can discuss and agree on global policies relating to the sustainable use and conservation of genetic resources for food and agriculture, and the fair and equal sharing of benefits resulting from their use. The commission oversaw the development of the Global Plan of Action for Animal Genetic Resources, as well as the two editions of the State of the World's Animal Genetic Resources for Food and Agriculture. The role of the working group is to review issues related to animal genetic resources and their management, to consider progress made in the implementation of the commission's programme of work, and to advise and make recommendations to the commission on all relevant matters relating to animal genetic resources. Twenty-eight countries make up the working group, with members elected at each of the commission's regular sessions. In our rapidly changing world, the diversity of animal genetic resources is going to play an increasingly critical role. Careful management of the diversity of animal genetic resources can help us address livestock challenges today and in the future, supporting livelihoods, strengthening resilience, and contributing towards food security, building a better world for us all.


We're going to go way back. Turn to page 163 in your workbook, please. And yeah, we're using the workbook again because it does a much better job. The other reason I use those photocopied notes, by the way, is they do combinatorics and probability in one less lesson than the workbook, so we gain two days, which is more handy than you realize, all right?  Certainly, I don't think it's on the same level as trigger logs. Sequences is what we're going to be looking at. So we're all on the correct page that I've said twice now, but I'll say it one more time. Page 163, page 163 under the B1, under the I6, under the M3, thank you, Elizabeth. Nice try trying to not look down and turn the page so no one would notice, but I caught that. Not as smooth as you thought. And now it's preserved for posterity on the internet. Now that I'm on YouTube, by the way, I'm getting people from all over North America subscribing to me, it seems, because I don't recognize any of the usernames. So you may be international. Woo-hoo! A sequence. A sequence is a number or a set of numbers in a definite order which are separated by commas. It's a group of numbers that have a pattern. The terms of a sequence are the values of some function whose domain is the set of natural numbers. That's a fancy way of saying, Jen, one of the things we're going to try and do is come up when we see a pattern of numbers with an equation that will generate any term without us having to write all the ones in front of it. So we're going to try and spot the pattern for the first four numbers. And I'm going to say, what's the 80th number? And please don't write the first 79. Come up with an equation. OK? A common way to define this function is by a formula which gives the nth term the generic term of a sequence. So let's start out. It says, write the next two terms of the following sequence and then describe a rule. Very basic. You've done this, hopefully, since you were children. Spot the pattern. What comes next? 9 comma 11. Now here is our terminology and our symbols. We call this first term, and I'm going to zoom in so I can write really small. We call this first term, term one. We call this second term, term two. So what would this guy be called? Term number what? Five or six? Which one? The 11. OK. This is term six. What I want to do is I want to write an equation so that when I put a six into the equation, the answer is 11. When I put a two into the equation, the answer is three. When I put a one into the equation, the answer is one. Sorry. OK. So here is Evan's suggestion. The nth term, the fifth term, the sixth term, the tenth term, the nth term is equal to 2n plus one. Now does that work? Let's see. If n is two, if I put a two there, I should get a three. Ah, 2n minus one. Does that work? Put a six in. Do you get an 11? Yes? Put a five in. Do you get a nine? So once I've done that now, Dina, I could say, hey, what's the 43rd term, and you don't need to write out the first 43 or 42, OK? This is the generic formula. By the way, Brendan, it's two times 43 minus one. It's your two times table. You're really reaching for your calculator? Really? It's your two times table. Come on. B. What comes next? 32, 64. So this is term one, term two, term three, term four, term five. This is term six. Is there an equation that if I put a six in, I get 64 back. If I put a five in, I get 32 back. Evan, you're on a roll, what? The nth term is two to the nth. Let's see. Two to the one is two. Two squared is four. Yeah, that works. What about C? What's the next term? 250. What's the next term? 125, OK. This is term one, term two, term three, term four, here's term five, here's term six. Can anybody come up with an equation so that when I put a six in it, I get 125 as an answer. When I put a five in it, I get a 250 as an answer. When I put a one in it, I get a 4,000 as an answer. You ready? This is the type of sequence we're going to look at this unit. It has a special name. It's called a geometric sequence. And it's a sequence where you're multiplying each term by the same number over and over. Now I know I'm dividing by two, but I want to talk about that in terms of multiplying. What am I multiplying each term by? What's the same as dividing by two? A half. This is a geometric sequence with a ratio of a half. And here is how you write the equation. Just watch first without writing down, see if you can figure out where I'm getting these numbers. Where does the 4,000 appear in the original sequence? First term. Where does a one-half appear in the original sequence? It's the common ratio, it's what I'm multiplying by. And then I added the n minus one because I've seen these before, but watch, Elizabeth. If you put a one right there, what's one take away one? Zero. What's anything to the zero power? A half? No. What's anything to the zero power? Ah. Putting a one in does give me a 4,000. It gives me 4,000 times one. Dillon, that's why I had to do an n minus one. If I want to put the first term there, put an n minus one there that gives me my first term. Let's try it for this one. Put a two there. Let's two take away one. One. What's one-half to the one? What's half of 4,000? Works. Ooh. Let's try a six. 4,000 times one-half, I'm going to type .5 to the what's six take away one. Will a six give me 125? Oh, I can hardly wait. Let's find out. Yes! We're going to come back to this special sequence here. A couple more just for practice because we're nerds. D, what's next? 13? What's next? 17? What's the pattern? By the way, if you could come up with an equation for that, you'll win the Nobel Prize for math. It hasn't been found yet. And we're interested because right now, all of your internet encryption, if you ever buy something online, your Visa card is encrypted, and the way it's encrypted is based on multiplying two huge prime numbers together. Prime numbers that are about 50 digits long because multiplying is much easier than going backwards and dividing. That result is used as what's called an RSA, public key encryption to encrypt your stuff. So if you did find a formula for that, although you would win the Nobel Prize for mathematics, it's called the Field Medal, by the way, you'd probably bankrupt the internet economy because now you wouldn't be able to encrypt credit cards. E, 8, 13, what's next? 21, what's next? 34, what are we doing? How do you find each term? Okay, so here's how I would write that. The nth term is equal to take the term before it and add the term to before it. I think that's how I'd write it. This is called a recursive sequence because it has T's on both sides. We're not looking at those. It's also called the Fibonacci sequence. If you've watched the Da Vinci Code or read the book, it's popular in there. Sadly, I knew of it long before that. So as soon as I saw those numbers in the book, I'd solved it already. It wasn't quite as exciting for me as it was for some people, but still. It shows up in weird places, the Fibonacci sequence, all over the place in nature. So the nth term, the nth term, the nth term, the nth term, we call that the general term of a sequence. It's the generic equation to generate a sequence. So the first term is written as T1, second term as term two. The two is subscripted, so you don't think you're multiplying. The general term or the nth term is written as Tm. The general term provides a formula which is used to describe any term of a sequence. For example, the first one Evan pointed out was the nth term is 2n-1. We break sequences first of all into two main types. Finite and infinite. Infinite has a dot, dot, dot, and that goes on forever. Finite often has a dot, dot, dot in the middle, but then they add a last term in what they're saying. Their DNA is, stop there! By the way, what's the first term in each of these sequences? Three, what are you multiplying by? Two, can you see the general term? It's first term times the ratio to the n-1. You're going to eventually not have to memorize that. It's on your formula sheet, but it's just really here. That works for any sequence that's generated by multiplying the same number over and over and over and breadth. Those are the ones we're going to spend some time on. Next page. Example A says, list the first three terms of this sequence. So, term 1, term 2, term 3. What this really means, Brett, is put a 1 in for n. So, what's 1 squared? Times 3, 3 minus 1. The first term of this sequence is 2, gamma. Madison, what's n for this one? 2, 2 squared. Times 3, minus 2. I guess the second term of this sequence is 10. Try finding the third term on your own. Your hint is it's 3 squared times 3 minus 3. 3 squared is 9. Is it that? B says, find the eighth term. How would I find the eighth term? Put an 8 in for n. n is the term number. I'm not going to bother. I said we break sequences into two types, infinite and finite. There's another way we break sequences. We divide sequences into how they're created. There are what are called arithmetic sequences, geometric, and others. Arithmetic, I think you did some in math temp where you're adding the same thing over and over. I'm not going to look at those. Well, it says the constant is called the common difference. What are you adding in each term here? Let's at least write that down. The common difference is 4. We're going to look at geometric sequences where you're multiplying the same thing over and over and over. We're going to say multiplying. If you're dividing by 3, we're not going to say that. We're going to say you're multiplying by 1 third. That way it lets us always write the same style of equation. We call what you're multiplying by the common ratio. What's the common ratio in this example here? How can you find the common ratio? Most of you are doing it intuitively, but if it's yucky, divide any term by the one in front of it and give you the common ratio. 6 divided by 2, or 18 divided by 6, or 15 divided by 18, either of those, pick whichever one's easiest. That's if it's a yucky one with decimals and you can't see the common ratio. Any term divided by the one in front of it. Then there's other sequences. We're not going to care about those. Example 3 says classify the following as arithmetic, geometric, or neither. I'm just going to circle the geometric ones. This one here, you're multiplying by 2. This one here, you're multiplying by a half. Those are the two geometric ones. So geometric sequences that we're going to focus on for the next four lessons. First thing you've got to be able to do. Amateur, you've got to be able to find the ratio. And often you'll just do it intuitively. What are we multiplying each number by here? I'm willing to bet not too many of you went 12 divided by 6. You just somehow saw it. That's the best way. R equals 2. But if you're not sure, any term divided by the one in front of it. Now this is not on your formula sheet so I won't do a big highlighted thing around it. But I'll be repeating that over and over. So what's the common ratio here? What's the common ratio here? Don't squint any term divided by the one in front of it. Dina, any term divided by the one in front of it. Now I'll simplify that. Any term divided by the one right in front of it. See how I got that? But what is negative divided by negative? What's 5 over 10 in lowest terms? In other words, if you can't just do it intuitively like we did here, any term divided by the one in front of it and pick the easiest two terms, I could also have gone negative 5 halves divided by negative 5. Why deal with fractions if you don't have to? Here's one they love to do. Put a little D before you turn the page. I like this question. I like this question. I like this question. Y squared over X, Y, X over Y. What's the common ratio? This is how they get around the fact that there are apps that you can download for the calculators that will do a lot of this for you. How can I always find the common ratio? Any term divided by one in front of it. I think I'm going to go this one divided by this one. Y divided by Y squared over X. You guys are all looking panicky. Oh, come on. Why don't I do that there? Did you say cross-multiply? Am I getting my baseball bat out? Am I going to have to freak on you? That's not cross-multiplying, Evan. Cross-multiplying is when you have one equation equals one. How do I divide by a fraction? You have never heard me say cross-multiply. You know what? I won't use a time sign because it's going to look like an X. I think the common ratio is that. Is it not? And I think you also get the same thing if you do it this way. Or do you? X divided by... Did I do this right? Oh, you know what? I should have done this. Erase the Y in the last term. That's better, I think. Negative 1X is 0X is 1X. 2Y is 1Y is 0. Yeah, there's the sequence. Sorry. Then that would have been a way smarter thing to do. Any term divided by the one in front of it. What's X divided by Y? It's that. That would have been an easier way to find the ratio. But they love to give you algebraic ones. They just don't like to make them up on the fly like I did because apparently it's too easy to make a dumbest rake. Sorry. Turn the page now. It says developing a formula to find the general term or towards the end of the year. If this was in October, I would actually develop the formula with you. Instead, I'm just going to go straight to the punchline. We're going to scroll down, down, down, down, down. Here's what we're going to say. This here is the formula for any geometric sequence. But we need to talk about what each letter means. Some of these letters, you already know what they mean. What does R mean? Ratio. What does N mean? The term number. Term 5. Term 7. Term 19. 342. And A is what we chose to use to represent the first term. Why do you think we picked the letter A to represent the first term? Yep. It's one that makes sense. That's all right here, by the way, but I've always found kids by writing it out, it jogs in their memory a bit more. Okay? So look up. How would I write this as a general equation? The nth term is equal to, Nick, what's the first term? A bracket. What's R? More specific in this. What's R to the n minus 1? Does that work? Let's see. The fourth term is a 24. If I put a 4 right there, what's 4 take away 1? 3. What's 2 cubed? 8 times 3. 24 works. Here you want to come up with the equation. The nth term is going to be, Amy, what's the first term? What's R? You know what I would do? I would use these two here because they're smaller numbers. Any term divided by the one in front of it. First of all, is R going to be negative or positive? Negative. And in lowest terms, kiddo? How about a half? Yep. 4.5. Either is acceptable to the n minus 1. So do you have to memorize this formula? No. It's on your formula sheet. You do got to know what the letters mean though. But I think they're picked fairly intelligently this time. In fact, you can think about a sequence this way. Madison, give me a number between 1 and 10. 7. There's the first number. 7. Dylan, give me a number between 1 and 4, including one or, but not, sorry, between 2 and 4 inclusive. Let's let R be 3. So 7, 21 times 3, 63 times 3, 189. If they gave me that, algebraically, algebraically with tally, I think of it as term 1, term 2, term 3, term 4. I think of it as A, first term, A times R, because if N is 2, R to the n minus 1 is just R. AR squared, AR cubed. Think of it that way. Next page. So you're ready? Example 5, do both of these on your own. Find the general term and then find term 7. It says, determine the general term and calculate the seventh term. And yes, this time you can use your calculators. I'll freeze the screen, see if you end up where I end up. There's the answer to A. See if you get the same thing. And by the way, it's customary to use fractions rather than decimals as your final answers. So the .008, whatever it was that you may get. Nope. Is it negative or positive? I'm sure. No, I think it's positive. Final answer is positive. 1 over 192, yeah? Skip 6. Example 7. Now, what I can also do is instead of saying here's the first couple. Find the general term. I can tell you a specific term at a location and find either A or R or M. So here's what I would like us to do. Write above example 7 where you have some blank space. Let's write down our generic equation, which is TN equals A, R to the N minus 1. That's what we put in the little box of the previous section. So it says, given this sequence, determine what's part A wanting me to find in this particular equation, which variable? David, N. That means they told me everything else. Let's see. Let's put an equal sign. Did they tell me A, the first term? What's that? Good. Did they tell me R, the common ratio? 2. You've already said I don't know Ns. I'll put the N minus 1 there. Did they tell me the Nth term? Did they tell me the term at the location that they want me to figure out? What? 16,384. Where is the variable sitting in an exponent? How do I solve an equation where the variable is in an exponent? Logs, baby! Oh, but wait a minute. We're not going to take the logs yet. We always want it to get the exponent by itself. I see right under there. Let's divide by 32 first. Divide by 32. Divide by 32. Our new equation is going to be 16,384. Divide it by 32. 512. I have 512 equals 2 to the N minus 1. Where is the N sitting as an exponent? Log both sides. The log of 512 equals the log of N minus 1. Why does the log help? What can I do with that exponent? Oh, pray tell. Isn't this great review? Where's the 2? I'll make it a little bigger so you can see. Sorry. And I think I actually forgot to write it. Sometimes my tablet's acting up. Sometimes I write stuff but it doesn't show up. You guys have occasionally seen me going, nothing's appearing for you. I don't think this time that was the case. What can I do with that exponent though, Madison? Move it to the front. In fact, I'll get this. The log of 512 equals N minus 1 in brackets because there's two terms. Log 2. Is that how to get the N by itself? How to get the N by itself? I think first I would divide by log 2 and then plus 1. In fact, N is going to be the log of 512 divided by the log of 2 plus 1. And it's been so long since you touched that log button. Many of you, why don't you all practice piping that in just so you can get familiar again with the procedure, right? Oh, by the way, N, because it's a term location, can't ever be a decimal.  It's not the third, the 3.5th term. That's the third term or the fourth term. What do you get? 10? B. So B is the same question as A. It's saying which term, really, which term number is 1024. So try this, but instead of a 16384, they're telling you the term is 1024 and see if you can solve for N on your own. It's a great review of logarithms. I'll do it slowly up here with the screen frozen. So, if I haven't said so already, I like that question. I like that question. I like that question. That's a great multiple-choice question. Find N. Oh, I'll even tell you what the answers would be for question B. Six, seven, or something else, silly. With the N minus one, the most common mistake, kids find N and it's one too big because they forgot the minus one. Example eight. I like this question. I like this question. I like this question. I like this question. I like this question. Absolutely going to be on your question. Now we're going one step further. Now they're telling me the fourth term, what's the fourth term of this sequence? And the seventh term, what's the seventh term of this sequence? Find the first term, the ratio, and the general term. We're actually going to find the ratio first. There are several ways to do this. Nick, there's a nerdy algebraic way and although my heart likes it, my head does not because I think there's an easier way and the easier way is to draw this.  What term number is this here? I don't know term one. I don't know term two. I don't know term three, term four. I don't know term five. I don't know term six, term seven. Write that down. It takes five seconds to draw that and it gives you a nice visual representation. And we're going to use this to get an equation. Once you've written that down, put your bets down because this is where we're going to get clever. Remember I said, we're going to find r first actually even though they said find the first term. I always find r first. So what did I multiply this number by to get that? I don't know but I know what I called it. What variable have I used for the thing that I multiply by? And you know what I multiply this number by? And you know what I multiply this number by? See how I drew the comma there? Because here's what Sav is really saying although he doesn't realize it yet.  Did I hear you say easy to solve? Yeah, how? Divide by negative 54 and then how do I get rid of a cubed? I like this method. There are other methods and systems that cross-multipline. I think the one second it takes to draw it, it falls apart so nicely. Does that make sense? Okay, Brett. Good. Find r. Oh, this is also a good chance for you to review where your cube root and fourth root and fifth root buttons are on your calculator because you're going to be using this great review. r cubed is going to be 1458 over negative 54. r is going to be the cube root of 1458 divided by negative 54. Now, technically, I know the answer to this without a calculator. I'm pretty sure it's negative three, but you should know where your cube root button is, so find the cube root and negative 27. Confirm for me that it is negative three. It is, yes? So, Megan, what if I'd given you this same statement? There's term four. There's terms instead of five, you know? There's the seventh, eight, nine. You could just hop Scott's your way. Or find the third term. You could going this way, you would divide. Oh, they want me to find the first term. Ready, Seth? What did I divide by if I'm going this way? What did I divide by if I'm going this way? What did I divide by if I'm going this way? It seems to me if I start with negative 54 and I divide by one, two, that many, I end up at the first term. Oh, and do I know what R is? That's why I said I always find R first. I think A is going to be negative 54 divided by negative three. Oh, no, negative three cubed or cubed. What's A? Two or negative two? Two. And you know what I tend to do just because I feel so proud that Tally, I tend to say, oh, not a T, Mr. DeWitt, a two. I know the first term. What's the last thing want me to find, the Tally? What's the third thing? The general term. Now the general term equation, which you don't have to memorize, it's on your sheet was the nth term is equal to A, R to the n minus one. So let's plug stuff in specifically for this particular sequence. The nth term is equal to what is A? We figured it out. What? Two. What's R? Negative three to the n minus one. There is the generic term to generate that sequence. So if we're, you know what I'm even going to say, Jen, if we're only medium clever, we can find whatever the heck they want to if they give us two terms. Am I ever going to give you like the third term and the 80th term? No, I'm not going to make you draw that much. It's going to be terms that are three or four or five apart. You'll end up doing a cube root of four through the fifth, through the sixth. That's my method. In the workbook, who has the solution manuals? He will use the algebraic cross multiply method if you don't like my method, use that one. It's so much fun. Turn the page. I like number nine. I like number nine. Number nine is a nice question. I like number nine. I like number nine. I like number nine. And here's what it says. X plus five and X plus nine are the first three terms in a geometric sequence, a sequence where you're multiplying by the same thing over and over. Find the exact value of each term. I think really what I'm going to do is find what X is and then just put it in for each of those. Hmm. Well, Sam, what did I multiply by to get from this term to this term? Algebraically, what variable have I got? What variable have I used? What did I multiply by to get from this term to this term? Algebraically, what variable have I used? So here's what I think that means.  It seems to me how can we find R if it's numbers? What did I say always works if you can't spot it? Any term, what? Divided by the term in front. It seems to me that X plus 5 divided by X equals R. It has to. Oh, and it seems to me that X plus 9 divided by X plus 5, any term, divided by the one in front of it. You know what that has to work out to? R. If those both equal R, what can we conclude? They equal each other. So I'm going to get the equation like this. X plus 5 over X has to equal X plus 9 over X plus 5. Any term, divided by the one in front of it has to equal any other term divided by the one in front of it. Evan, how will I solve this equation, oh, pray tell? What's this a wonderful example of? This is cross-multiplying. You got it, baby. I'm going to rewrite this as X plus 5, X plus 5. Oh, this is going to be a quadratic. It will be nearly cool. X times X plus 9. Now what? Freeze up and lose marks? No, no, no. You've done the hard part. Now what? Factoring is when you write it with brackets. We want to do the opposite of factoring. Our acronym for that is usually FOIL. Get rid of brackets. So the right-hand side is easier. X squared plus 9X. The left-hand side, X plus, oh, this is FOIL. I think X squared plus 10X plus 25. What kind of an equation is this? Now, I thought it was going to be a quadratic. Actually, it's not, because what's going to happen to the X-squareds when I try getting them to the same side? When I minus X squared from both sides, it's going to vanish. I thought I might have two values for X and two possible Rs that worked. I like that question. I like that question. But here, I think Dina, cancel. Cancel. In fact, Jen, I have 10X plus 25 equals 9X. I'm going to minus 10X from both sides. I get 25 equals negative X. I think X equals negative 25. So if they want the first three terms, and it's based on this pattern, what's X? What's the first term, also X? Negative 25. What's the second term? Negative 20. Negative 25 plus 5. What's the third term? Negative 16. What's R? If I ask that instead. Any term divided by the one in front of it, so negative 16 over negative 20, positive, reduce the fraction. What's the seventh term? Now that I know A and R, could I find term 7? Yeah. I mean, whatever they need. Sorry. But this algebraic one where there's three terms with X's in each of them and you don't know X. I like that because it's reminding you you do know R. It's any term divided by the one in front of it. And any pair of Rs has to be equal to each other. One more. Do you know what I mean by that? I can't call the math easy exactly, but you've got to learn some stuff.  A geometric mean. Does anybody know what does the word mean in math? It's a fancy word for average. So, a geometric mean is a fancy term for the terms being put between a geometric sequence. And it's harder to explain than to show. Jen, can you read example 10 to me please? Here's what this means. Starting with 81, and ending at 129, you know how many numbers they want us to put between them? Four. They want us, Jen, to do one, two, three, four and one over 729. That's inserting four geometric means. What if they said three geometric means three numbers? Saf, does this look kind of similar to this one here? So, Saf, my friend, I ask you, hey, what did I multiply this by to get to there? I need to come up with an equation that has a little d in the middle so it could be r, d, r, r, d, r, d. Saf, my friend, how many r's are there to get to 1 over 729? Can you tell me what equation I'm going to leap to? Starting with an 81, r to the fifth equals, come on, 7, there we go, 729. How would I get the r to the fifth by itself? r to the fifth equals 1 over 729 divided by 81. Math, enter, enter. Oh, it won't do this one as a fraction for me. Now, I still can do this as a fraction. When I divide by 81, isn't that just like putting an extra 81 at the bottom? The denominator of this fraction is going to be 729 times 81. It's going to be 1 over 59049. That's r as a fraction. You okay how I got that, Jim? Dividing is same as just multiplying it onto the denominator. How do I get rid of a fifth? Fifth root? r equals the fifth root of 1 over 59049. Now, I wonder if it'll work with the decimal let's see. Fifth root, oh, where's fifth root? Math. Oh, I got to type 5 first. Fifth root. Math, option 5 of that answer. Ah, you know what r is? 1 9th. So, you ready? Let's put the numbers in between. How would I find the first one? 81 times 1 9th. 9. And then take this answer times 1 9th. 1 times 1 9th. I think that's 1 9th, is it not? And I think the last one is 1 over 81. I could also have just divided by 9 each time along the way. There they are. Geometric sequences where you're multiplying by a common ratio.  And n is the term number, the number of terms. Tn is the actual term of value. What's your homework? How do I get the r to the 5th by itself? So, dividing by 81 is the same as putting an extra 81 down there. If you go 81 times 7 29, that's what that is. That, as the decimal, but if this was multiple choice, the fraction would be the answer to Pickrum. Now, of course, you'd be clever enough to take those fractions and change the decimals and see which one matched your decimal, but still. Is that okay? Brett. Number 2. Number 3. So 2 and 3. 5, 2, 3, 5, 6. Take a look at b. What is the last sentence of b? Explain what how much you want to bet this time you do get a quadratic where there's two x-values that work. Unlike the quadratic where we had that canceled out. 8, 9, 10, and 11. Everybody do this. That's how many more lessons. Because 4, take away 1 is 3. We are in the home stretch.


All right, well moving back to the U.S. as we saw in yesterday's story from our voices of the American South series, medical costs, hospital closures, opioid addiction and insurance woes, those have all left health care and poverty stricken Southern Appalachia and dire straits. Today Michael Schor continues his reporting, taking a look at the creative solutions that that region is coming up with in the face of crisis. A different kind of health care is lighting the way through the poverty, opioids and limited resources of Appalachia like a headlamp through a coal mine. This is the only substitute they have, the only way they have to get the proper health care. It's a major blessing. Now to that health. Coburn Virginia resident Jerry Kaiser is talking about the health wagon. A mobile medical provider transforming the way health care is delivered here. Right now we have 4900 patients that call the health wagon their home and we've had somewhere around 19,000 patient encounters. Dr. Joe Smitty runs the faith based health wagon, the creation of sister Bernie Kenny in 1980. He says the need for this is profound. Health care is getting worse all the time. I've worked here 40 years and it's dramatically worse. It was a prostate issue that brought Jerry's brother and roommate Mac to Dr. Paula Hill Collins at the health wagon. You know, my PSA's come down to zero and fit one for the health wagon, Paul and the doctors, you know, I probably wouldn't be here. Mac Kaiser served in Vietnam earned four purple hearts, a bronze star and a medal of valor. When you think about what you've done for the country and now what you have to do for your health care, how does that make you feel? It hurts, you know, but I just sometimes I crowd. People are making decisions about, you know, do I pay for my electricity to stay warm? Do I have food to eat? So many variables play into it. When we take the health wagon out, we're actually bringing the service closer to the community. There is a wide community of those doing this work in this area, like remote area medical or RAM, the original creation of Stan Brock, whose first clinic in the US was in Sneedville, Tennessee in 1992. From those humble beginnings, RAM has increased and grown to doing over 65 clinics a year domestically over 45,000 patients. We caught up with RAM senior coordinator Poppy Green at a clinic in Maryland, but he spends most of his time in these mountains. Often will see patients who arrive a couple days before the clinic is set to open. Those patients, we think about that wait time in the parking lot, but many of them have been waiting years. RAM CEO Jeff Eastman says dental care is a major focus. So about two out of three people come in seeking dental help. About a third come in for vision. Teeth are what bring Yvonne Evans to work at RAM. If they don't know that they have a bad tooth or if they have one, they'll go in the garage and take pliers out and take the tooth out. A RAM clinic recently saw over 1400 patients in nearby Gray, Tennessee just before we visited with Dr. Smitty. Does it amaze you that in the United States you have 1400 people lining up to get health care because they don't have it themselves? What we have in America is flimsy excuses for why why those folks aren't cared for. The worst lie of all is you can go to any emergency room in America and receive any health care you need. But in places like Lee County, Virginia, there isn't an ER within reach of so many of the residents. The only hospital for miles closed in 2013. A core group of Lee County residents took it upon themselves to establish a hospital authority board and they have been working diligently ever since to reopen this hospital. Quite honestly at that time, it really seemed hopeless. Mark Lenderton, Howard Elliott are talking about the Ballad Health Facility set to open this year as a full hospital. Today, the nearest hospital is over an hour away. We know that we have lost citizens in the back of an ambulance on the way to distant hospital. So I think that the need is greater than what's realized. Stacey Ealy gave us a tour of the still shuttered facility that will be resuscitated because the hospital authority made it happen. They kept the lights on, they kept the boilers going, they kept the utilities on which kept this building in great shape. So Ballad Health is coming into a great facility. We are currently standing where the future inpatient beds will be. But sometimes it's more than just hospital beds. Sometimes Dr. Smitty just pulls out a banjo instead of a stethoscope. And that's medicine no one else is giving.  But here in the mountains, it works, works like a charm. I asked Henry Vires what gratitude sounds like from the folks he serves. What a blessing it is to have you. That's the kind of things you hear. That's the kind of things you see. That's the kind of things we love. And that is just what we saw. Michael Shour, I-24 News in Southwestern Virginia. And joining us now from Los Angeles, our senior national correspondent, Michael Shour. Michael, great series. Let me ask you, healthcare was an issue that Democrats felt really boosted them in the last midterms. Now going into the next election, you've been down there looking at this situation in what is traditionally red states, Republican country, Trump country. How much do you think is healthcare going to be a fact, do you think, going into the 2020 election? You know, it's really interesting. The way you frame that too, Kolev, because this is very red country. Both of those areas where we were are represented by Republican members of Congress in Tennessee and Virginia. It is solidly red country yet by the same token. There are so many people that are left out in healthcare, whether you're in Iowa or whether you're in New Hampshire or whether you're in that part of Appalachia or Appalachia, either pronunciation accepted. You will find people who say that healthcare is the number one issue. It still polls as the number one issue, but it's also a place that is very deeply religious. And so there is a conundrum for many of these people as to how they vote, who will have their best interest when they get to Washington. And so far, the Republicans have been able to lean on the former military and lean on the religious vote in those places. But as healthcare becomes a worsening crisis there, I think more people are waking up to that. And such an important crisis to be focusing on, especially when there is so much distraction, some legitimate, some not, with so much else. Michael, what else can we be looking forward to from the series? Yeah, you know, just on that point, Noree, because it's really true what you say. You go to these places, they're not thinking about Iran. When you heard Henry Vires there say that they're deciding whether to put food on their table, pay their electric bill, or go to a doctor. These are not people that are thinking about Iran when they wake up in the morning. So there is a real divide between what we're talking about a lot and what these people are living. Tomorrow, we will be talking about the issue of vaping. You know, the U.S. government centered in Washington and New York to some degree. But the Centers for Disease Control is in the South, and a lot of what they do is focused on the South. And we're going to talk about that and how that's affecting the South and emergency treatment for that. So it should be an interesting story tomorrow. Noree Kalev. Michael, just before we let you go, you've done a lot of reporting on the ground in various communities across the U.S., whether it's political stories or otherwise. I'm interested just in, you know, what this was like for you. Were you surprised at all by some of what you saw and heard in these communities? Eye-opening. And again, Noree, you point that out, is perceptive. I've never been to that part of America, and it's a place that is as forgotten as they say it is. And when you see, and I asked Dr. Smitty about it, 1,500 people lining up to get health care in America with all that we have here in this country, it really is eye-opening. It's depressing as well. You see small towns. We were in a place called Pennington Gap in Virginia, and you couldn't believe how desperate folks are there. And the streets, the downtown, if you want to call it that, it's eye-opening stuff. The fact that these people are there, that there is still hope in the ashes there, I think that is actually also very encouraging. These are people who go to work to try and make things better there every day. And that is, that's an important takeaway that we all had. Jeff Mills, who is our photographer there, producers Alex Rhodes and Tatiana Diaz, as we looked at this stuff, we saw some hope through what, through Jeff's lens and also through the stories that they were telling us. Yes, the great creative solutions they were coming up with. Unfortunate, obviously, that they have to even come up with something like that, as you said, in America, but still the power of community. Michael Schur, thanks so much for that. And with that, that is it for us, right?


Hello and welcome back to my channel! If you're new here, my name is Jackie and I'm an aspiring writer, and in this video I want to share with you how I'm planning to track my writing in 2021. Now this was inspired by a blog post that Brandon Sanderson does every year called The State of Sanderson, where he goes through the year that's passed and everything that he's put out and his status updates and so on. And I read his update for 2020, and one of the first things he says is, I keep track of this by doing a big spreadsheet, and I thought, I like spreadsheets, I like tracking, and I've done spreadsheets in the past, generally when I'm doing NaNoWriMo or Camp NaNoWriMo because the website is only really good for tracking word count, and there are other things I want to track. So I thought, why not take my existing spreadsheet and just use it for the whole year? And I thought this would be really interesting for tracking not only the amount I write throughout the year, but how my writing ebbs and flows throughout the year, how productive I am on different projects or how long different projects take, how productive I am at different times of the day or using different tools, and even how productive I am at different stages of my menstrual cycle because last year I did a couple of videos on basically trying to optimize my life and my writing for my menstrual cycle, which I'll link to in the description. So in my spreadsheet, the columns are day and date of course, sleep I actually just added this morning because last night I had a really bad night of sleep. I went to bed and of course immediately had an idea about the story I'm working on. So I ended up giving up on sleeping and writing that. And then when I tried to get back to sleep, it was 1am and our neighbor was shoveling snow at 1am. And one of the problems when you live in a foreign country and can't speak the languages, you can't go out and tell them to stop because I don't have that vocabulary in Russian or Estonian. So that was rather annoying.  The time that I spend writing or working on my projects, the activity, so whether I'm writing, outlining, revising and so on, the productive time. So I have this distinct to the writing session because sometimes you can have a session where you get distracted or you might go into a research black hole and so on.  So I want to know how much of the time I'm spending at the computer is productive time. Now, depending on how disciplined I am with tracking that, that is probably going to be not so accurate because in the past when I've tried to do that really accurately, I've had like a pen and paper next to me and every time I've stopped actively writing, I've written down what the time is and every time I start writing again then I write down what the time is so at the end I can go through the session and go okay how much time was actually spent writing. In reality I'm probably not going to do that every time but at the end of a session I have a good idea of okay I spent you know half of that time writing or a third of that time writing or and so on so probably be guesstimating that one. Then of course the words written in a day, I haven't decided whether I'm going to split up the rows into sessions rather than days because some days I might have more than one writing session at the moment I've just got one row per day so words written and then words per minute so that's the number of words divided by the number of productive minutes, number of scenes completed and then the length of the scene this is based on the number of scenes completed divided by the number of words written time to complete the scene. This is something I haven't decided how helpful it is yet but I thought it would be helpful to have more things to measure than just pure word count such as how I'm progressing through scenes. Total time spent so this is the cumulative time I spent writing and working on writing related things throughout the year total words written again cumulative total the project that I'm working on so the project I'm working on at the moment is my fantasy hot mess when that changes to something else obviously there'll be something else in this column cycle phase tools used so at the moment I've got them back into using four the words which is a monster battle writing tool and the reason I have this tools used column is just to see if there are certain tools that work really well for certain activities and getting stuff done and then finally any notes so for the current project it is not a first draft it's a third draft or third and a half draft I'm not really sure but I am writing it that there are some things that I will copy from the last draft such as nice description or some nice dialogue and so on even though I'm expecting the bulk with the book and the organization will be new so one of the reasons why I want to have notes here is because if I have a day when I get really really high words per minute or a really high total word count maybe it's because I copied 5,000 words from the old document so that should be noted so I know the reason for any outliers if there are outliers then on the second tab of the spreadsheet I have my charts so I might add to this over time but at the moment there's a heim tracker which is just the cumulative amount of time total words the daily words so that's a bar where each day you'll see the number of words and it'll be interesting to see how much variation there is over time and then writing efficiency so this is the words per minute I might also come up with some other measures to measure writing efficiency but at the moment words per minute is the best one I've got and that is an overview of how I'm going to be tracking my writing in 2021 so let me know do you use any tools like this to track your writing if so what do you use what are the different things you like to track like word count time spent and so on and are there any other tools or tricks you have for staying focused so that when you have a session it's predominantly productive time rather than you have three hours and only one hour of it was spent writing so please let me know what you used to help with your writing productivity in the comments if you like this video give me a like hit the notification bell hit the subscribe button and I will see you next time bye