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JEE Main & Advanced Mathematics Sequence & Series Question Bank Relation between AP., GP. and HP.

  • question_answer
    If \[a,\ b,\ c\] are in A.P. and \[a,\ b,\ d\] in G.P., then \[a,\ a-b,\ d-c\] will be in  [Ranchi BIT 1968]

    A) A.P.

    B) G.P.

    C) H.P.

    D) None of these

    Correct Answer: B

    Solution :

    Given that \[a,\ b,\ c\] are in A.P. \[\Rightarrow b=\frac{a+c}{2}\] ?..(i) and \[{{b}^{2}}=ad\] ?.. (ii) Hence \[a,\ a-b,\ d-c\] are in G.P. because \[{{(a-b)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}=a(a-2b)+ad\] \[=a(a-a-c)+ad=ad-ac\].


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