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