An infinite G.P. has first term $‘x’$ and sum is 5 then $x$ belongs to

Let$r$ be the common ratio of the G.P. Then

$-1<r<1$.

Now,

$\begin{array}{l}\text{ Sum }=5\\ \Rightarrow \frac{x}{1-r}=5\\ \Rightarrow 1-r=\frac{x}{5}\\ \Rightarrow r=1-\frac{x}{5}\end{array}$

$\Rightarrow -1<1-\frac{x}{5}<1 [\because -1<r<1]$

$\Rightarrow -2<-\frac{x}{5}<0\Rightarrow 2>\frac{x}{5}>0\Rightarrow 10>x>0\Rightarrow 0<x<10$