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BCECE Engineering BCECE Engineering Solved Paper-2005

  • question_answer
    If a, b, c are in AP, a, mb, c are in GP, then \[a,{{m}^{2}}b,c\]care in:

    A)  HP                                         

    B)  GP                         

    C)         AP                         

    D)         none of these

    Correct Answer: A

    Solution :

    Since, a, b, c are in AP, then \[2b=a+\text{ }c\]                                 ...(i) and \[a,\text{ }mb,\text{ }c\]are in GP, then \[mb=\sqrt{ac}\]                 or            \[{{m}^{2}}{{b}^{2}}=ac\]                     ?(ii) From Eqs. (i) and (ii)                                 \[\frac{{{m}^{2}}{{b}^{2}}}{2b}=\frac{ac}{a+c}\]                 \[\Rightarrow \]    \[{{m}^{2}}b=\frac{2ac}{a+c}\] \[\Rightarrow \]    \[a,{{m}^{2}}b,c\]are in HP.


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