First slide

Introduction to statistics

Question

The geometric mean of $3, 3^{2} \dots, 3^{n}$ is

Easy

A

$3^{n / 2}$
B

$3^{(n + 1) / 2}$
C

$3^{n (n + 1) / 2}$
D

none of these

Solution

$\begin{array}{l} G.M. = {(3 \cdot 3^{2} \cdot 3^{3} \dots 3^{n})}^{1 / n} \\ = {(3^{1 + 2 + \dots + n})}^{1 / n} = {(3 \frac{n (n + 1)}{2})}^{1 / n} \\ = 3^{(n + 1) / 2} \end{array}$

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