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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Sequences and Series

NDA 2018 · Mathematics · Sequences and Series

If an infinite GP has the first term x and the sum 5 , then which...

If an infinite GP has the first term xx and the sum 5 , then which of the following is correct?

Options

  1. Ax<−10\mathrm{x} < -10
  2. B−10<x<0-10 < \mathrm{x} < 0
  3. C0<x<100 < x < 10
  4. Dx>10x > 10

Correct answer

C. 0<x<100 < x < 10

Step-by-step solution

Sum of an infinite G.P. with first term xx and common ratio r(<1)r( < 1) is s=x1−rs=\frac{x}{1-r} From question s=5s=5 then, 5=x1−r5=\frac{x}{1-r}1−r=x5r=1−x5\begin{aligned} 1-r & =\frac{x}{5} \\ r & =1-\frac{x}{5} \end{aligned}For, $-1 < 1-\frac{x}{5} < 1\begin{aligned} -2 & < -\frac{x}{5} < 0 \\ 0 & < x < 10 \end{aligned}$$$
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