Question

The $G.M$ of the numbers $3,3^2,3^3,\dots ,3^{3n}$ is

• A. $3^{\frac{n}{2}}$
• B. $3^{\frac{3n}{2}}$
• C. $3^{\frac{3n+1}{2}}$
• D. $3^{\frac{n+1}{2}}$

Answer 1

Answer: (C)

$GM$ . of $3^1,3^2,3^3,\dots ,3^{3n}$
$={\left(3\cdot 3^2\cdot 3^3\dots 3^{3n}\right)}^{\frac{1}{3n}}={\left(3^{1+2+3+\dots +3n}\right)}^{\frac{1}{3n}}$
$=3^{\frac{3n\left(3n+1\right)}{2\cdot 3n}}=3\frac{3n+1}{2}$