Question

Sum of infinite term of G.P is $20$ and sum of their square is $100$ then common ratio of G.P. is

• A. $5$
• B. $\frac{3}{5}$
• C. $\frac{8}{5}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $\frac{3}{5}$

Let terms of G.P are $a,ar,a{r}^2,...$

$\therefore S_{\infty }=\frac{a}{1-r}$

$a=$first term,

$r=$common ratio

$S_{\infty }=20$ [Given]

According to question $\frac{a}{1-r}=20$

$\Rightarrow a=20(1-r)$ ........(i)

also $\frac{a^2}{1-r^2}=100$

$\Rightarrow \frac{a}{1-r}.\frac{a}{1+r}=100$

$\Rightarrow a=5(1+r)$ .........(ii)

Divide (i) by (li)

$\frac{a=20(1-r)}{a=5(1+r)}$

we have $r=\frac{3}{5}$