Question

An infinite G.P. has first term as x and sum upto infinity as $5$. Then the range of values of 'x' is :

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

Answer 1

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

Solution -

$x,xr,x{r}^2----\infty$

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

$-1<r<1$

$x=5-5r$

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

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

$0<x<10$

C is correct