Solveeit Logo
Login

Question

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

32/n3^{2/n}

B

3(n−1)/23^{(n - 1)/2}

C

3n/23^{n/2}

D

3(n+1)/23^{(n + 1)/2}

Answer

3(n+1)/23^{(n + 1)/2}

Explanation

Solution

G.M.=(3.32.33.......3n)1/n= (3.3^{2}.3^{3}.......3^{n})^{1/n}

=(31+2+.......n)1/n=(3n(n+1)2)1/n=3n+12= (3^{1 + 2 + .......n})^{1/n} = \left( 3^{\frac{n(n + 1)}{2}} \right)^{1/n} = 3^{\frac{n + 1}{2}}.