Question

In an infinite G.P., if the first term is $x$ and sum of all terms is $5$, then

• A. $x\in (0,10)$
• B. $x\in [1,10]$
• C. $x\in (10,\infty )$
• D. $x\in (-\infty ,0)$

Answer 1

The correct option is A $x\in (0,10)$

Let $r$ be the common ratio, so
$\frac{x}{1-r}=5\Rightarrow r=1-\frac{x}{5}$

We know that,
$|r|<1\Rightarrow -1<1-\frac{x}{5}<1\Rightarrow -2<-\frac{x}{5}<0\Rightarrow -10<-x<0\Rightarrow 0<x<10\therefore x\in (0,10)$