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

NDA 2018 · Mathematics · Sequences and Series

If the second term of a GP is 2 and the sum of its infinite term is...

If the second term of a GP is 2 and the sum of its infinite term is 8 , then the GP is

Options

  1. A8,2,12,18,……8,2, \frac{1}{2}, \frac{1}{8}, \ldots \ldots
  2. B10,2,25,225,……10,2, \frac{2}{5}, \frac{2}{25}, \ldots \ldots
  3. C4,2,1,12,122,……4,2,1, \frac{1}{2}, \frac{1}{2^2}, \ldots \ldots
  4. D6,3,32,34,……6,3, \frac{3}{2}, \frac{3}{4}, \ldots \ldots

Correct answer

C. 4,2,1,12,122,……4,2,1, \frac{1}{2}, \frac{1}{2^2}, \ldots \ldots

Step-by-step solution

Let the first term and common ratio of the G.P. is a and rr respectively. Then, ar=2,a1−r=8a r=2, \frac{a}{1-r}=8⇒arr−r2=8⇒2=8r−8r2⇒4r2−4r+1=0⇒r=12\begin{aligned} & \Rightarrow \quad \frac{a r}{r-r^2}=8 \\ & \Rightarrow \quad 2=8 r-8 r^2 \\ & \Rightarrow \quad 4 r^2-4 r+1=0 \\ & \Rightarrow \quad r=\frac{1}{2} \end{aligned}∴\therefore G.P. is 4,2,1,12,…4,2,1, \frac{1}{2}, \ldots
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