Question

The Geometric mean of $4,4^2,4^3,\cdots ,4^n$ is

• A. $2^{\frac{n}{2}}$
• B. $2^{\frac{n+1}{2}}$
• C. $4^{n+1}$
• D. $2^{n+1}$

Answer 1

The correct option is D $2^{n+1}$

Required geometric mean $={({4.4}^2{.4}^3{.4}^4...........{.4}^n)}^{1/n}$
$={\left(4^{1+2+3+\mathrm{4........}+n}\right)}^{1/n}=4^{(n+1)/2}=2^{n+1}$