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NDA 2019 Maths · Mathematics · Sequences and Series · medium

In a GP the fourth term is 24 and the seventh term is 192. The sum of the first eight terms is

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In a GP the fourth term is 2424 and the seventh term is 192192. The sum of the first eight terms is
  1. A. 381381
  2. B. 765765
  3. C. 765/2765/2
  4. D. 15301530
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Answer: (B) 765765

Dividing, r3=19224=8r^3=\dfrac{192}{24}=8, so r=2r=2. Then ar3=24a r^3=24 gives a=3a=3. The sum is S8=3(28−1)2−1=3×255=765S_8=\dfrac{3(2^8-1)}{2-1}=3\times255=765. The value 381381 is the sum of the first seven terms, which is the trap when counting terms, and 15301530 doubles the correct answer.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake