Question

Geometric mean of the numbers $2, 2^2, 2^3, ... , 2^n$ is

• A. $2^{2/n}$
• B. $2^{n/2}$
• C. $2^{\frac{n - 1}{2}}$
• D. $2^{\frac{n + 1}{2}}$

Answer 1

Answer: (D)

Geometric mean
$ = \left(2\times2^{2} \times2^{3}\times....\times 2^{n}\right)^{1/n}$
$ = \left(2^{1+2+3+...+n}\right)^{1/n} $
$= \left[2^{\frac{n\left(n+1\right)}{2}}\right]^{\frac{1}{n}} = 2^{\frac{n+1}{2}} $