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

  • question_answer
    If \[p,\ q,\ r\] are in one geometric progression and  \[a,\ b,\ c\] in another geometric progression, then \[cp,\ bq,\ ar\] are in [Roorkee 1998]

    A) A.P.

    B) H.P.

    C) G.P.

    D) None of these

    Correct Answer: C

    Solution :

    As \[p,\ q,\ r\] are in G.P. \[\therefore \]\[{{q}^{2}}=pr\] ?..(i) and \[a,\ b,\ c\] are also in G.P. \[\therefore \]\[{{b}^{2}}=ac\] ?..(ii) From (i) and (ii), \[{{q}^{2}}{{b}^{2}}=(pr)(ac)\]\[\Rightarrow \]\[{{(bq)}^{2}}=(cp)\ .\ (ar)\] Hence \[cp,\ bq,\ ar\] are in G.P.


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