Question

The sum of infinite $G.P$ is $6$. If the first term is $2$, its common ratio.

Answer 1

Sum of infinite G.P. $=6$

First term $\left(a\right)=2$

Common ratio $\left(r\right)=?$

As we know that sum of infinite G.P. is-

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

Therefore,

$6=\frac{2}{1-r}$

$\Rightarrow 6-6r=2$

$\Rightarrow 6r=6-2$

$\Rightarrow r=\frac{4}{6}=\frac{2}{3}$