The G.M of the numbers $3^{1}, 3^{2}$ , $3^{3}$ , ..., $3^{3 n}$ is

3^{\frac{n}{2}}

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3^{\frac{3 n}{2}}

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3^{\frac{3 n + 1}{2}}

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3^{\frac{n + 1}{2}}

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Solution

The correct option is C $3^{\frac{3 n + 1}{2}}$
$G . M . o f 3^{1}, 3^{2}, 3^{3}, 3^{4} . . . . . 3^{3 n} = (3^{1} \times 3^{2} \times 3^{3} \times 3^{4} . . . . 3^{3 n})^{\frac{1}{3 n}} = 3^{\frac{3 n + 1}{2}}$

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