JEE Main & Advanced Mathematics Sequence & Series Question Bank Arithmetico - Geometric Series, Method of difference

  • question_answer
    If \[a,\ b,\ c\] are in H.P., then which one of the following is true [MNR 1985]

    A) \[\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{b}\]

    B) \[\frac{ac}{a+c}=b\]

    C) \[\frac{b+a}{b-a}+\frac{b+c}{b-c}=1\]

    D) None of these

    Correct Answer: D

    Solution :

    \[a,\ b,\ c\] are in H.P. \[\Rightarrow \]\[b=\frac{2ac}{a+c}\] By inspection, we get (a) False (b) False (c) False


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