Mathematics - Sequence & Series Question with Solution | TestHub

If $b$ is the first term and $r$ is the common ratio of an infinite G.P. and sum is $5$, then

$5=\frac{b}{1-r}$

$\Rightarrow 1-r=\frac{b}{5}$

$\Rightarrow r=1-\frac{b}{5}$

$\Rightarrow r=\frac{5-b}{5}$

$\therefore -1<r<1$

$\therefore -1<\frac{5-b}{5}<1$

$\Rightarrow -5<5-b<5$

$\Rightarrow -10<-b<0$

$\Rightarrow 0<b<10$

$\Rightarrow b\in \left(0, 10\right)$