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Question

What is the geometric mean of the sequence 1,2,4,8,......2n?

A
2n/2
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B
2(n+1)/2
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C
2(n+1)1
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D
2(n1)
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Solution

The correct option is C 2n/2
Given:
G.M.=(1.2.4.8......2n)1n+1

G.M.=(20.21.22.23......2n)1n+1

G.M.=(20+1+2+3+...+n)1n+1

G.M.=((2)n(n+1)/2)1n+1

G.M.=2n/2



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