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NDA 2018 Maths · Mathematics · Sequences and Series · medium

In a harmonic progression the 3rd term is 1/5 and the 6th term is 1/11. What is the 9th term?

Single correct option

In a harmonic progression the 3rd term is 15\dfrac15 and the 6th term is 111\dfrac1{11}. What is the 9th term?
  1. A. 115\dfrac1{15}
  2. B. 117\dfrac1{17}
  3. C. 119\dfrac1{19}
  4. D. 114\dfrac1{14}
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Answer: (B) 117\dfrac1{17}

Reciprocals form an AP: 3rd term 5, 6th term 11, so 3d=63d=6, d=2d=2. The 9th AP term is 11+3⋅2=1711+3\cdot2=17, hence the HP term is 1/171/17. Forgetting to take the reciprocal at the end is the usual error.
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Original question written in the NDA 2018 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