Question

The first term of an infinite geometric progression is x and its sum is 5. Then

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$5=\frac{x}{1-r}$
$\Rightarrow 5-5r=x\Rightarrow r=1-\frac{x}{5}$
As $|r|<1$ i.e., $|1-\frac{x}{5}|<1-1<1-\frac{x}{5}<1$
$-5<5-x<5=-10<-x<0=10>x>0$
i.e., $0<x<10.$