JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

Let

A_1, G_1, H_1

denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For

n>2

, let

A_{n-1}

and

H_{n-1}

have arithmetic, geometric and harmonic means as

A_n, G_n, H_n

respectively. Then, which one of the following statements is correct?

View answer and explanation

Correct option: C

G_1=G_2=G_3=\ldots

Option C (G1=G2=G3=...) is correct because the geometric mean remains constant in this recursive process.

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