The G.M. of the numbers 3, , 3^2 , , 3^3 ,...., , 3^n is - Vidyadip

MCQ

The $G.M.$ of the numbers $3,\,{3^2},\,{3^3},....,\,{3^n}$ is

A
${3^{\frac{2}{n}}}$
✓
${3^{\frac{{n + 1}}{2}}}$
C
${3^{\frac{n}{2}}}$
D
${3^{\frac{{n - 1}}{2}}}$

✓

Answer

Correct option: B.

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

b
(b) $a = 3, r = 3$

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

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

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