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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  Statistics
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Geometric mean of $ 1, 2, 2^2, 2^3.....2^n$ is

$\begin {array} {1 1} (A)\;2^{\large\frac{2}{n}} & \quad (B)\;2^{\large\frac{n}{2}} \\ (C)\;2^{\large\frac{n-1}{2}} & \quad (D)\;2^{\large\frac{n+1}{2}} \end {array}$

 

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1 Answer

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G.M = $ ( 1.2^1.2^2.2^3......2^n)^{ \large\frac{1}{n+1}}$
$ = (2^{1+2+3+....+n}) ^{\large\frac{1}{n+1}}$
$ = \bigg[ 2 ^{\large\frac{n(n+1)}{2}} \bigg]^{\large\frac{1}{n+1}}$
$ = 2^{\large\frac{n}{2}}$
Ans : (B)
answered Jan 25, 2014 by thanvigandhi_1
 

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