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Question: The G.M. of the numbers \(3,3^{2},3^{3}......3^{n}\) is...

The G.M. of the numbers 3,32,33......3n3,3^{2},3^{3}......3^{n} is

A

32n3^{\frac{2}{n}}

B

3n+123^{\frac{n + 1}{2}}

C

3n23^{\frac{n}{2}}

D

3n−123^{\frac{n - 1}{2}}

Answer

3n+123^{\frac{n + 1}{2}}

Explanation

Solution

G.M. of

(3.32.33......3n)=(3.32.33......3n)1/n=(3)1+2+3+....+nn=3n(n+1)2n=3n+12(3.3^{2}.3^{3}......3^{n}) = (3.3^{2}.3^{3}......3^{n})^{1/n} = (3)^{\frac{1 + 2 + 3 + .... + n}{n}} = 3^{\frac{n(n + 1)}{2n}} = 3^{\frac{n + 1}{2}}