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Stage: 3 Challenge Level: Challenge Level:1


Here are the first few sequences from a family of related sequences:
$A_5 = 32, 96, 160...$
$A_6 = 64...$
$A_7 = ...$

Which sequences will contain the number 1000?
Once you've had a chance to think about it, click below to see how three different students began working on the task.
Alison started by thinking:

"I have noticed that each number is double the number in the row above. I wonder if I can work out what would go in the rows above 1000?"


Bernard started by thinking:

"I have noticed that in $A_1$, the numbers which end in a 0 are 10, 30, 50... If I carry on going up in 20s I won't hit 1000, so I know 1000 isn't in $A_1$."

Charlie started by thinking:

"I have noticed that each number in $A_1$ is 2 more than a multiple of 4. I know 1000 is $250 \times 4$ so it can't be in $A_1$."



Here are some further questions you might like to consider:
Do all positive whole numbers appear in a sequence?
Do any numbers appear more than once?
Which sequence will be the longest?  