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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Sequences and Series

NDA 2010 · Mathematics · Sequences and Series

The sum of an infinite geometric progression is 6. If the sum of...

The sum of an infinite geometric progression is 6. If the sum of the first two terms is 9/29 / 2, then what is the first term?

Options

  1. A1
  2. B5/25 / 2
  3. C3 or 3/23 / 2
  4. D9 or 3

Correct answer

D. 9 or 3

Step-by-step solution

Given a+ar=92a(1+r)=92a+a r=\frac{9}{2}a(1+r)=\frac{9}{2}...(i)  Again 6=a1−r∴a=6(1−r)...(ii)\begin{array}{rlrl}\text{ Again } 6 & =\frac{a}{1-r} \\ & \therefore \quad a & =6(1-r)...(ii)\end{array}\begin{aligned}& \text{ from (i) }6\left(1-r²\right)=\frac{9}{2}\\ & \begin{aligned}-12 r² & =-3 \\ r & = \pm \frac{1}{2}\\ \therefore \quad a & =6\left(1-\frac{1}{2}\right)=3 \text{ or }6\left(1+\frac{1}{2}\right)=9 \\ a & =9 \text{ or }3 .\end{aligned}\end{aligned}
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