Question

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

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

Answer 1

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

$\frac{x}{1-r}=5\Rightarrow r=1-\frac{x}{5}$
Since G.P. contains infinite terms
$\therefore -1<r<1\Rightarrow -1<1-\frac{x}{5}<1\Rightarrow -2<-\frac{x}{5}<0\Rightarrow -10<-x<0.\Rightarrow 0<x<10.$