Question

An infinite G.P has first term 'x' and sum '5' , then x belongs to :

• A. $|x|<10$
• B. $-10<x<0$
• C. $0<x<10$
• D. $x>10$

Answer 1

The correct option is C $0<x<10$

We know that the sum of infinite terms of GP is

$S_{\infty }=\{\begin{array}{c}\frac{a}{1-r};\left|r\right|<1\\ \infty ;\left|r\right|\ge 1\end{array}$

$\therefore S_{\infty }=\frac{x}{1-r}=5$ since $\left|r\right|<1$

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

$\Rightarrow -1<\frac{5-x}{5}<1$

$\Rightarrow -5<5-x<5$

$\Rightarrow -10<-x<0$

$\therefore 0<x<10$