Question

The geometric mean if the series $1,2,4,....,2^n$, is

• A. $2^{n+\left(1/2\right)}$
• B. $2^{(n+1)/2}$
• C. $2^{n-\left(1/2\right)}$
• D. $2^{n/2}$

Answer 1

Answer: (D)

$2^{n/2}$

$1,2,4,.....,2^n$

No. of terms $=n+1$

$\therefore G.M.=({\mathrm{1.2.4......2}}^n{)}^{\frac{1}{n+1}}$

$=(2^{1+2+3+...+n}{)}^{\frac{1}{n+1}}$

$=(2{)}^{\frac{n(n+1)}{2}.\frac{1}{n+1}}$

$=2^{n/2}$