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)

$G M$ . of $3^{1}, 3^{2}, 3^{3}, \ldots, 3^{3n}$
$=\left(3\cdot3^{2}\cdot3^{3}\ldots3^{3n}\right)^{\frac{1}{3n}}=\left(3^{1+2+3+\ldots+3n}\right)^{\frac{1}{3n}}$
$=3^{\frac{3n\left(3n+1\right)}{2\cdot3n}}=3\frac{3n+1}{2}$