NDA 2022 Maths · Mathematics · Sequences and Series · medium

If n arithmetic means are inserted between a and b, their sum is (n(a+b))/(2). 2. The geometric mean of two distinct positive numbers is greater than…

Single correct option

Consider the following statements:
1. If

n

arithmetic means are inserted between

a

and

b

, their sum is

\frac{n(a+b)}{2}

.
2. The geometric mean of two distinct positive numbers is greater than their arithmetic mean.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (A) 1 only

Statement 1 is true: the

n

means plus the end terms form an AP, and the means are symmetric about the average

\frac{a+b}{2}

. Statement 2 is false: AM exceeds GM for distinct positive numbers.

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