Help with Resistance Homework: Finding Sum to Infinity

[JJYEO325]

Homework Statement

The first term of a convergent g.p is 3. The sum of the first five terms of the progression is twice the sum of the first ten terms. Find the sum to infinity of the progression.

Homework Equations

S(5)= 3(r^5 -1)/4
S(10)=3(r^10 -1)/9
.
.
.
8^10-9r^5+1=0
Sum to infinity= 8.8

The Attempt at a Solution

But the answer is 1.60

 

[Mentallic]

How did you get

$$S_5=\frac{3\left(r^5-1\right)}{4}$$

It should be,

$$S_5=\frac{3\left(r^5-1\right)}{r-1}$$

Firstly set up your summations correctly, and use the info that is given - mainly:

The sum of the first five terms of the progression is twice the sum of the first ten terms.

This should give you an equality in r, which can then be solved. Then use the infinite summation formula.