Question

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

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

Answer 1

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

Given:-

$S_{\infty }=5$

$a=x$

As we know that,

$S_{\infty }=\frac{a}{1-r}$

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

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

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

Now,

$\left|r\right|<1$

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

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

$\Rightarrow -2<\frac{-x}{5}<0$

$\Rightarrow 0<\frac{x}{5}<2$

$\Rightarrow 0<x<10$