What is the geometric mean of 3, 3^2, 3^3, do | vedclass

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(C) The geometric mean of $n$ terms $a_1, a_2, \dots, a_n$ is given by $(a_1 	imes a_2 	imes \dots 	imes a_n)^{1/n}$.Here,the terms are $3^1, 3^2,

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

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(C) The geometric mean of $n$ terms $a_1, a_2, \dots, a_n$ is given by $(a_1 	imes a_2 	imes \dots 	imes a_n)^{1/n}$.Here,the terms are $3^1, 3^2, 3^3, \dots, 3^n$.Their product is $P = 3^1 	imes 3^2 	imes 3^3 	imes \dots 	imes 3^n = 3^{(1+2+3+\dots+n)}$.The sum of the first $n$ natural numbers is $\frac{n(n+1)}{2}$.So,$P = 3^{n(n+1)/2}$.The geometric mean is $P^{1/n} = (3^{n(n+1)/2})^{1/n} = 3^{(n+1)/2}$.

What is the geometric mean of $3, 3^2, 3^3, \dots, 3^n$?

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