CA Foundation · Quantitative Aptitude · Sequence and Series
The reciprocals of the terms of a sequence form an arithmetic progression 3, 5, 7, 9, ... Hence the sequence 1/3, 1/5, 1/7, ... is a harmonic progression. What is its 10th term?
The 10th term is 1/21. The reciprocals 3, 5, 7, ... form an AP with first term 3 and common difference 2, so the 10th reciprocal is 3 + 9×2 = 21. Taking the reciprocal of that AP term gives the required harmonic progression term.
- A1/21Correct
- B1/23
- C1/19
- D1/29
Explanation
A sequence is an HP when its reciprocals are in AP. The reciprocal AP has first term 3 and common difference 2, so its 10th term is 3 + 9×2 = 21. The 10th HP term is therefore 1/21. The option 1/23 comes from using 10 differences instead of 9.
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