JEE Main & Advanced Mathematics Statistics Question Bank Mean

  • question_answer
    The G.M. of the numbers \[3,\,{{3}^{2}},\,{{3}^{3}},\,......,\,{{3}^{n}}\] is                 [Pb. CET 1997]

    A)                 \[{{3}^{2/n}}\]       

    B)                 \[{{3}^{(n-1)/2}}\]

    C)                 \[{{3}^{n/2}}\]       

    D)                 \[{{3}^{(n+1)/2}}\]

    Correct Answer: D

    Solution :

                       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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