SOLUTION: Given that the first term and the common ratio of a geometric sequence are 3/8 and -2 respectively, and the sum of the first n terms is -8,191.875, find the sum of the (n+1) term t

Algebra ->  Sequences-and-series -> SOLUTION: Given that the first term and the common ratio of a geometric sequence are 3/8 and -2 respectively, and the sum of the first n terms is -8,191.875, find the sum of the (n+1) term t      Log On


   

Question 1188018: Given that the first term and the common ratio of a geometric sequence are 3/8 and -2 respectively, and the sum of the first n terms is -8,191.875, find the sum of the (n+1) term to the (n+5) term.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


S(n) = a+ar+ar^2+...+ar^(n-1)

S(n) = a(1+r+r^2+...+r^(n-1)

S%28n%29+=+a%28%281-r%5En%29%2F%281-r%29%29

We are given a=3/8, r=-2, and S(n) = -8191.875. Plug the numbers into the formula to determine n.


1-%28-2%29%5En+=+8%28-8191.875%29=-65535
-%28-2%29%5En+=+-65536+=+-2%5E16
n=16

We are to find the sum of the (n+1) term to the (n+5) term, or the sum of the 17th to 21st terms, which is S(21)-S(16).

S%2821%29+=+%281%2F8%29%28%281-%28-2%29%5E21%29%29+=+262144.125

And then

S%2821%29-S%2816%29+=+262144.125-%28-8191.875%29+=+270336

ANSWER: 270336