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
${3^{2/n}}$
B
${3^{(n - 1)/2}}$
C
${3^{n/2}}$
✓
${3^{(n + 1)/2}}$

✓

Answer

Correct option: D.

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

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

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

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

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

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