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NDA 2025 Maths · Mathematics · Sequences and Series · easy

The reciprocals of the terms of an AP (with non-zero terms) form an AP. 2. The reciprocals of the terms of a GP (with non-zero terms) form a GP.

Single correct option

Consider the following statements:
1. The reciprocals of the terms of an AP (with non-zero terms) form an AP.
2. The reciprocals of the terms of a GP (with non-zero terms) form a GP.
Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (B) 2 only

Statement 2 is true: reciprocals of a,ar,ar2,…a,ar,ar^2,\dots are 1a,1ar,…\frac1a,\frac1{ar},\dots with ratio 1r\frac1r. Statement 1 is false: reciprocals of an AP form an HP, e.g. 1,2,31,2,3 gives 1,12,131,\frac12,\frac13, which is not an AP.
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Original question written in the NDA 2025 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