Sum of infinite number of terms of a G.P.

Question

Sum of infinite number of terms of a G.P. is 20, and the sum of their squares is 100. The common ratio of the G.P. is:

Accepted Answer

$\dfrac{a}{1-r}=20\Rightarrow a=20(1-r)$. Also $\dfrac{a^2}{1-r^2}=100$.

$$\frac{[20(1-r)]^2}{(1-r)(1+r)}=100 \Rightarrow \frac{400(1-r)}{1+r}=100 \Rightarrow 4(1-r)=1+r \Rightarrow 5r=3 \Rightarrow r=\frac35.$$

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