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CA Foundation · Quantitative Aptitude · Sequence and Series

The 3rd term of a harmonic progression is 1/7 and its 6th term is 1/13. What is the 10th term of the progression?

The 10th term is 1/21. The reciprocals of an HP form an AP, with third term 7 and sixth term 13, giving common difference 2. Seven more steps from the third term give 7 + 14 = 21, so the 10th HP term is 1/21.

  1. A1/19
  2. B1/21
  3. C1/23Correct
  4. D1/20

Explanation

Reciprocals form an AP: third term 7, sixth term 13. So 3d = 6 and d = 2. The 10th reciprocal term is 7 + 7×2 = 21, so the 10th term of the HP is 1/21. Option 1/23 would result from using 8 steps of d instead of 7... but the key distractor 1/19 comes from counting only 6 steps from the third term.

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