Question

An infinite G.P. has first term $x$ and sum $5.$ Then which of the following is true

• A. $0<x<10$
• B. $0<x<15$
• C. $x>10$
• D. $x>5$

Answer 1

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

Let $r$ be the common ratio
Given $\frac{x}{1-r}=5$
$\Rightarrow r=1-\frac{x}{5}$
But, we have $|r|<1$
$\Rightarrow -1<1-\frac{x}{5}<1\Rightarrow -2<-\frac{x}{5}<0\Rightarrow -10<-x<0\Rightarrow 0<x<10$