Question

If $b$ is the first term of an infinite $G.P.$ whose sum is five, then $b$ lies in the interval :

• A. $(-\infty ,-10]$
• B. $(-10,0)$
• C. $(0,10)$
• D. $[10,\infty )$

Answer 1

The correct option is C $(0,10)$

We know that,
$\frac{b}{1-r}=5\Rightarrow 1-\frac{b}{5}=r$
Now,
$-1<r<1\Rightarrow -1<1-\frac{b}{5}<1\Rightarrow -2<-\frac{b}{5}<0\Rightarrow -10<-b<0\Rightarrow 10>b>0$