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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