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

  • question_answer
    An A.P., a G.P. and a H.P. have the same first and last terms and the same odd number of terms. The middle terms of the three series are in

    A) A.P.

    B) G.P.

    C) H.P.

    D) None of these

    Correct Answer: B

    Solution :

    Let \[a\] and \[b\] be the same first and last terms of the three progressions, each having \[(2n+1)\] terms. Then the middle term of the A.P. is\[\frac{a+b}{2}\]. The middle term of the G.P. is\[\sqrt{ab}\]. The middle term of the H.P. is\[\frac{2ab}{a+b}\]. Obviously, these terms are in G.P.


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