Gujarati
8. Sequences and Series
easy

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

A

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

B

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

C

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

D

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

Solution

(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}}}$.

Standard 11
Mathematics

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