The geometric mean of the numbers $7, 7^{2}, 7^{3}, . . ., 7^{n}$ is

7^{7 / 4}

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7^{4 / 7}

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7^{\frac{n - 1}{2}}

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

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Solution

The correct option is D $7^{\frac{n + 1}{2}}$
Required geometric mean $= ({7.7}^{2} {.7}^{3} . . . . . . . . {.7}^{n})^{1 / n} = (7^{1 + 2 + 3 + . . . . . . . + n})^{1 / n} = 7^{\frac{n + 1}{2}}$

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