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NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Sequences and Series

NDA 2014 · Mathematics · Sequences and Series

The sum of an infinite GP is x and the common ratio r is such that...

The sum of an infinite GP is xx and the common ratio rr is such that ∣r∣<1|r| < 1. If the first term of the GP is 2 , then which one of the following is correct?

Options

  1. A−1<x<1-1 < x < 1
  2. B−∞<x<1-\infty < x < 1
  3. C1<x<∞1 < x < \infty
  4. DNone of the above

Correct answer

C. 1<x<∞1 < x < \infty

Step-by-step solution

 First term of G.P. =a=2 and common ratio =rSum of ∞ terms =a1−r=21−r∵−1<r<1∴−1<x<1 is correct answer. \begin{aligned} & \text{ First term of G.P. }=a=2 \text{ and common ratio }=r \\ & \text{Sum of } \infty \text{ terms }=\frac{a}{1-r}=\frac{2}{1-r} \\ & \because-1 < r < 1 \\ & \therefore-1 < x < 1 \text{ is correct answer. }\end{aligned}
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