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JEE Advanced 2007Paper 2

Exam: JEE Advanced
Year: 2007
Paper: Paper 2
Subject: Mathematics
Chapter: Sequences and Series

JEE Advanced 2007 · Paper 2 · Mathematics · Sequences and Series

Paragraph: Let A_1, G_1, H_1 denote the arithmetic, geometric and...

Paragraph: Let

A_1, G_1, H_1

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

n \geq 2

, let

A_{n-1}

and

H_{n-1}

has arithmetic, geometric and harmonic means as

A_n, G_n, H_n

, respectively.Question: Which of the following statements is correct?

Options

A $\mathrm{H}_1>\mathrm{H}_2>\mathrm{H}_3>\ldots$
B $H_1 < H_2 < H_3 < \ldots$
C $H_1>H_3>H_5>\ldots$ and $H_2 < H_4 < H_6 < \ldots$
D $\mathrm{H}_1 < \mathrm{H}_3 < \mathrm{H}_5 < \ldots$ and $\mathrm{H}_2>\mathrm{H}_4>\mathrm{H}_6>\ldots$

Correct answer

B. $H_1 < H_2 < H_3 < \ldots$

Step-by-step solution

As above

A_1>H_2>H_1, A_2>H_3>H_2

\therefore \quad H_1 < H_2 < H_3 < \ldots

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