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

  • question_answer
    The numbers \[(\sqrt{2}+1),\ 1,\ (\sqrt{2}-1)\] will be in  [AMU 1983]

    A) A.P.

    B) G.P.

    C) H.P.

    D) None of these

    Correct Answer: B

    Solution :

    The numbers \[({{a}_{1}}+{{a}_{24}})+({{a}_{5}}+{{a}_{20}})+({{a}_{10}}+{{a}_{15}})=225\] will be in G.P. \[\therefore \] \[{{(1)}^{2}}=(\sqrt{2}+1)(\sqrt{2}-1)={{(\sqrt{2})}^{2}}-{{(1)}^{2}}=2-1=1\].


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