The geometric mean of numbers 7-72- 73- - -7 n is-A- 77-nB- 7n-7C- 7n-1-2D- 7n-1-2

The correct option is D The G.M of numbers 7,7^2, 7^3, .......7^n (7,7^2, 7^3, .......7^n )^1/n=(7^1+2+3+....+n)^1/n = ( 7 n(n+1)/2 )^1/n =7^ (n 1)/2 ...

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Byju's Answer

Standard XII

Mathematics

Geometric Mean

The geometric...

Question

$T h e g e o m e t r i c m e a n o f n u m b e r s 7, 7^{2}, 7^{3}, . . . . . . {.7}^{n} i s :$

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Solution

The correct option is D
$T h e G . M o f n u m b e r s 7, 7^{2}, 7^{3}, . . . . . . {.7}^{n} (7, 7^{2}, 7^{3}, . . . . . . {.7}^{n})^{\frac{1}{n}} = (7^{1 + 2 + 3 + . . . . + n})^{\frac{1}{n}} = {(7 \frac{n (n + 1)}{2})}^{\frac{1}{n}} = 7^{\frac{(n - 1)}{2}}$

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The geometric mean of numbers 7,72,73,.......7n is:

The correct option is D The G.M of numbers 7,72,73,.......7n(7,72,73,.......7n)1n=(71+2+3+....+n)1n=(7n(n+1)2)1n=7(n−1)2

$T h e g e o m e t r i c m e a n o f n u m b e r s 7, 7^{2}, 7^{3}, . . . . . . {.7}^{n} i s :$

The correct option is D
$T h e G . M o f n u m b e r s 7, 7^{2}, 7^{3}, . . . . . . {.7}^{n} (7, 7^{2}, 7^{3}, . . . . . . {.7}^{n})^{\frac{1}{n}} = (7^{1 + 2 + 3 + . . . . + n})^{\frac{1}{n}} = {(7 \frac{n (n + 1)}{2})}^{\frac{1}{n}} = 7^{\frac{(n - 1)}{2}}$