SOLUTION: A geometric progression has a third term equal to 48 and fifth term equal to 768. a. Find the possible values of the common ratio. b. Find the sum of the first seven terms of

Algebra ->  Sequences-and-series -> SOLUTION: A geometric progression has a third term equal to 48 and fifth term equal to 768. a. Find the possible values of the common ratio. b. Find the sum of the first seven terms of      Log On


   

Question 1183578: A geometric progression has a third term equal to 48 and fifth term equal to 768.
a. Find the possible values of the common ratio.
b. Find the sum of the first seven terms of the geometric
progression, taking the positive value of the common ratio.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
g%5B3%5D+=+48 and g%5B5%5D+=+768, along with the fact that g%5B5%5D+=+r%5E2%2Ag%5B3%5D ===> 768+=+48r%5E2 ===> r%5E2+=+16
===> r+=+%2B-+4. <--- part (a)
Now g%5B3%5D+=+48+=+g%5B1%5D%2Ar%5E2+=+16g%5B1%5D ===> g%5B1%5D+=+3.
The sum of the first n terms of a geometric series is given by the formula

S%5Bn%5D+=+g%5B1%5D%2A%28%281-r%5En%29%2F%281-r%29%29

===> S%5B7%5D+=+3%2A%28%281-4%5E7%29%2F%281-4%29%29+=+16383 <--- part (b)