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Question

The geometric mean of 1,2,22,.....,2n is


A

2n2

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B

nn+12

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C

2n(n+1)2

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D

2n-12

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Solution

The correct option is A

2n2


Explanation for the correct option:

Compute the geometric mean of the given geometric progression.

A geometric progression 1,2,22,.....,2n is given.

It is clear that the given geometric progression has n+1 terms.

So, the Geometric mean G.M is as follows:

G.M=1·2·22·....·2n1n+1⇒G.M=21+2+3+...+n1n+1⇒G.M=2n(n+1)21n+1⇒G.M=2n2 [∵Since the sum of n natural numbers is n(n+1)2]

Therefore, the geometric mean of the given geometric progression is 2n2.

Hence, option A is the correct option.


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