Question

An infinite G.P. has first term as $a$ and sum as $5$ , then

• A. $a<-10$
• B. $-10<a<10$
• C. $0<a<10$ and $a\ne 5$
• D. $a>10$

Answer 1

Answer: (C)

$S_{\infty }=\frac{a}{1-r}=5($ given $)$
$\Rightarrow r=\frac{5-a}{5}$
But $0<|r|<1$
$\Rightarrow 0<\left|\frac{5-a}{5}\right|<1$
$\Rightarrow -1<\frac{5-a}{5}<1$ and $a\ne 5$
$\Rightarrow -5<5-a<5$ and $a\ne 5$
$\Rightarrow -10<-a<0$ and $a\ne 5$
$\Rightarrow 10>a>0$ and $a\ne 5$
$\Rightarrow 0<a<10$ and $a\ne 5$