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JEE Main & Advanced Mathematics Sequence & Series Question Bank Self Evaluation Test - Sequences and Series

  • question_answer
    What is the product of first 2n + 1 terms of a geometric progression?

    A) The (n + 1)th power of the nth term of the GP

    B) The (2n + 1)th power of the nth term of the GP

    C) The (2n + 1)th power of the (n + 1)th term of the GP

    D) The nth power of the (n + 1)th terms of the GP

    Correct Answer: C

    Solution :

    [c] The GP is a, \[ar,a{{r}^{2}},......a{{r}^{2n}}\] So,  \[P=a.\,ar..a{{r}^{2}}.a{{r}^{3}}........a{{r}^{2n}}\] \[={{a}^{2n+1}}.{{r}^{1+2+......+2n}}\] \[={{a}^{(2n+1)}}r\,{{\,}^{\frac{2n(2n+1)}{2}}}={{a}^{2n+1}}{{r}^{n(2n+1)}}={{(a{{r}^{n}})}^{(2n+1)}}\] \[=(2n+1)th\] power of the \[(n+1)th\] term of GP.


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