Question:
A geometric progression has first term a (where a > 0), and common ratio r. The sum of the first n terms is Sn and the sum to infinity is S. Given that S2 is twice the value of the fifth term, find the value of r. Hence find the least value of n such that Sn is within 5 % of S.
Thank you for helping!
Hello, Tangera!
Are you sure of the wording of the problem?
It doesn't seem to be solvable.
A geometric progression has first term , and common ratio
The sum of the first terms is and the sum to infinity is
Given that is twice the value of the fifth term, find the value of
Hence find the least value of such that is within 5% of
is the sum of the first two terms: .
The fifth term is: .
We have: .
. . which factors: .
We know that , and the cubic has no rational roots.
Now what?