SOLUTION: A geometric progression has a positive common ratio,and the sixth term is (5/4)^4,The sum of the first three terms and the sum of the third,fourth and fifth terms are in the ratio

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Question 1040863: A geometric progression has a positive common ratio,and the sixth term is (5/4)^4,The sum of the first three terms and the sum of the third,fourth and fifth terms are in the ratio 16:25.Find the sum of the first three terms?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
1) a%5B6%5D+=+%285%2F4%29%5E4, and
2) S%5B3%5D%2F%28a%5B3%5D%2Ba%5B4%5D%2Ba%5B5%5D%29+=+16%2F25.
From #2,
==>
=
=1%2Fr%5E2+=+16%2F25 ==> r%5E2=25%2F16 ==> r= 5/4, since r > 0 as stipulated.
==> a%5B6%5D+=+a%5B1%5D%2Ar%5E5+=+%285%2F4%29%5E4

==> a%5B1%5D%2A%285%2F4%29%5E5+=+%285%2F4%29%5E4 ==> a%5B1%5D+=+4%2F5
==>