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11th Class Mathematics Sequence and Series Question Bank Sequence and Series (A.P., G.P. and H.P.)

  • question_answer
    If the three terms p, q, t are the\[{{\text{m}}^{\text{th}}}\],\[{{\text{n}}^{\text{th}}}\] and \[~{{\text{s}}^{\text{th}}}\]terms of GP. Then, the value of \[{{p}^{n-s}}.{{q}^{s-m}}.{{r}^{m-n}}\]

    A)  1       

    B)  2                

    C)  4                                

    D)  0

    Correct Answer: A

    Solution :

    (a): Let GP be \[a,ar,a{{r}^{2}}\] p = mth term \[\to a{{r}^{m-1}}\] q = nth term \[\to a{{r}^{n-1}}\] t = sth term \[\to a{{r}^{s-1}}\] \[\therefore \] \[{{p}^{n-s}}\,\,{{q}^{s-m}}\,\,{{r}^{m-n}}=\left( {{a}^{n-s}}.{{a}^{s-m}}.{{a}^{m-n}} \right)\] \[\times \left[ {{r}^{(m-1)(n-s)}}\times {{r}^{(n-1)(s-m)}}\times {{r}^{(s-1)(m-n)}} \right]\] \[={{a}^{(n-s+s-m+m-n)}}\times \left[ {{r}^{(m-1)(n-s)+(n-1)(s-m)+(s-1)(m-n)}} \right]\] \[={{a}^{0}}\times {{r}^{0}}=1\]                 


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