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NDA 2017 Maths · Mathematics · Sequences and Series · medium

In a harmonic progression the 2nd term is 1/3 and the 5th term is 1/9.

Single correct option

In a harmonic progression the 2nd term is 13\frac13 and the 5th term is 19\frac19. The 8th term is
  1. A. 112\dfrac1{12}
  2. B. 118\dfrac1{18}
  3. C. 115\dfrac1{15}
  4. D. 113\dfrac1{13}
Show answer and solution

Answer: (C) 115\dfrac1{15}

Reciprocals form an AP: 3 and 9 at positions 2 and 5, so 3d=63d=6, d=2d=2. The 8th reciprocal is 9+3×2=159+3\times2=15, so the 8th term is 115\frac1{15}. Forgetting to take the reciprocal at the end gives 15.
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Original question written in the NDA 2017 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