The G.M. of the numbers 3,32,33…,3n is

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

A
$3^{2 / n}$
B
$3 \frac{n - 1}{2}$
C
$3^{n / 2}$
D
$3^{\frac{n + 1}{2}}$

Solution:

Clearly,

Required GM $= {(3 \times 3^{2} \times 3^{3} \times \dots \times 3^{n})}^{1 / n}$

$\Rightarrow$ Required GM = $= {\{3^{1 + 2 + \dots + n}\}}^{1 / n} = {[3^{\frac{n (n + 1)}{2}}\}}^{1 / n} = 3^{\frac{n + 1}{2}}$

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