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

  • question_answer
    If \[x,\ 1,\ z\] are in A.P. and \[x,\ 2,\ z\] are in G.P., then \[x,\ 4,\ z\] will be in [IIT 1965]

    A) A.P.

    B) G.P.

    C) H.P.

    D) None of these

    Correct Answer: C

    Solution :

    \[x,\ 1,\ z\] are in A.P., then  \[2=x+z\] ......(i) and \[4=xz\] ......(ii) Divide (ii) by (i), we get \[\frac{x\ .\ z}{x+z}=\frac{4}{2}\]or \[\frac{2xz}{x+z}=4\] Hence \[x,\ 4,\ z\] will be in H.P.


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