Geometric mean of $7, 7^{2}, 7^{3} . . . . 7^{n}$ is

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

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7^{n / 2}

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

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7^{⎛ ⎝ \frac{n + 1}{3} ⎞ ⎠}

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Solution

The correct option is A $7^{\frac{(n + 1)}{2}}$
$G m$ of two no $a$ & $b = \sqrt{a b}$
For $a G P$
$G M = \sqrt{a_{1} . a n}$
$\Rightarrow G M$ of $7, 7^{2}, . . . . . 7^{n}$
$= \sqrt{{7.7}^{n}}$
$= 7 \frac{(n + 1)}{2}$

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