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NDA 2017 Maths · Mathematics · Sequences and Series · medium

For two distinct positive numbers, AM>GM>HM. 2. An infinite GP with first term 2 and common ratio 1.5 has sum -4.

Single correct option

Consider the following statements.

1. For two distinct positive numbers, AM>GM>HMAM>GM>HM.
2. An infinite GP with first term 2 and common ratio 1.5 has sum −4-4.

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: (A) 1 only

Statement 1 is a standard inequality for distinct positive numbers, so it is true. In statement 2 the formula a1−r\frac{a}{1-r} gives −4-4 but works only when ∣r∣<1|r|<1; with r=1.5r=1.5 the series diverges, so no sum exists. Only statement 1 is correct.
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Original question written in the NDA 2017 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