• # question_answer The first term of an infinite geometric progression is $x$ and its sum is 5. Then [IIT Screening 2004] A) $0\le x\le 10$ B) $0<x<10$ C) $-10<x<0$ D) $x>10$

Correct Answer: B

Solution :

$5=\frac{x}{1-r}$ $\Rightarrow$ $5-5r=x$ $\Rightarrow$  $r=1-\frac{x}{5}$ As $|r|\,<\,1$  i.e.,  $\left| \,1-\frac{x}{5}\, \right|<1$ $-1<1-\frac{x}{5}<1$ $-5<5-x<5=-10<-x<0=10>x>0$ i.e,  $0<x<10$.

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