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IIT JEE Advanced 2007 Paper 2

Paragraph Type

This section contains 2 paragraphs. Based on the paragraph, there are 3 questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Questions 58–60: 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}

has arithmetic, geometric and harmonic means as

A_n, G_n, H_n

, respectively.

Section: Mathematics

Question : 59 of 66

Marks: +1, -0

Which one of the following statements is correct?

[JEE Adv 2007 P2]

$A_1$ > $A_2$ > $A_3$ > …
$A_1$ < $A_2$ < $A_3$ < …
$A_1$ > $A_3$ > $A_5$ > … and $A_2$ < $A_4$ < $A_6$ < …
$A_1$ < $A_3$ < $A_5$ < … and $A_2$ > $A_4$ > $A_6$ > …

Validate

Solution:

Since

A_2

is the A.M. of

A_1

and

H_1

and

A_1

H_1

, we get

A_1

A_2

H_1

(1)

Also,

A_3

is the A.M. of

A_2

and

H_2

and

A_2

H_2

. Therefore,

A_2

A_3

H_2

⇒

A_1

A_2

A_3

> ...

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