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NDA 2023 Maths · Mathematics · Sequences and Series · medium

The 10th term of the harmonic progression 1/3,1/5,1/7,… is

Single correct option

The 10th term of the harmonic progression 13,15,17,…\dfrac13,\dfrac15,\dfrac17,\dots is
  1. A. 121\dfrac1{21}
  2. B. 119\dfrac1{19}
  3. C. 123\dfrac1{23}
  4. D. 2121
Show answer and solution

Answer: (A) 121\dfrac1{21}

The reciprocals 3,5,7,…3,5,7,\dots form an AP with a=3a=3, d=2d=2. The 10th reciprocal is 3+9×2=213+9\times2=21, so the 10th term of the HP is 121\dfrac1{21}. Option 2121 forgets to invert; 119\dfrac1{19} is the 9th term.
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Original question written in the NDA 2023 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