NDA 2021 Maths · Mathematics · Sequences and Series · medium

The arithmetic mean of two distinct positive real numbers is greater than their geometric mean. 2. If a,b,c are in harmonic progression, then…

Single correct option

Which of the statements is/are correct? 1. The arithmetic mean of two distinct positive real numbers is greater than their geometric mean. 2. If

a,b,c

are in harmonic progression, then

b=\dfrac{a+c}{2}

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Answer: (A) 1 only

Statement 1 is AM-GM with strict inequality for distinct numbers. For an HP,

1/a,1/b,1/c

are in AP, so

b=\dfrac{2ac}{a+c}

, not

\dfrac{a+c}{2}

; statement 2 is false. Only 1 is correct.

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