Insert into GP

Between numbers 5 and 640, insert as many numbers to form geometric progression so the sum of the numbers you entered will be 630. How many numbers must you insert?

Correct answer:

m =  6

Step-by-step explanation:

a1=5 an=640 sn=630+640+5=1275 an=a1qn1 sn=qn1q1  128=qn1=qn/q 1275=qn1q1  1275=5128q1q1 1275q1275=5(128q1) 635q=1270 q=2  128=qn1 ln128=(n1)ln2 n=8  m=n2=82=6



Tips to related online calculators


Related math problems and questions:

  • Sum of GP members
    exponentialFexsDecay Determine the sum of the GP 30, 6, 1.2, to 5 terms. What is the sum of all terms (to infinity)?
  • Geometric progression
  • Three members GP
  • Remainders
  • Sum 1-6
    seq_sum Find the sum of the geometric progression 3, 15, 75,… to six terms.
  • Bricklayers
  • Sum of series
  • Exponential equation
  • The raw
  • Six speeds
  • Terms of GP
    exp_growth What is the 6th term of the GP 9, 81, 729,. .. ?
  • Sequences AP + GP
    seq_sum The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. Find AP and GP members.
  • Short cut
    direct_route Imagine that you are going to a friend. That path has a length 120 meters. Then turn doprava and go other 630 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
  • In the 8
    seq In the A. P. 36, 39, 42, …, which term is 276?
  • Geometric progression
  • Loan 5
  • Finite arithmetic sequence
    seq_sum How many numbers should be inserted between the numbers 1 and 25 so that all numbers create a finite arithmetic sequence and that the sum of all members of this group is 117?