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

  • question_answer
    If \[a,\ b,\ c\] are in A.P., then \[{{3}^{a}},\ {{3}^{b}},\ {{3}^{c}}\] shall be in [Pb. CET 1990]

    A) A.P.

    B) G.P.

    C) H.P.

    D) None of these

    Correct Answer: B

    Solution :

    As given \[2b=a+c\] \[\Rightarrow {{3}^{2b}}={{3}^{a+c}}\] or \[{{({{3}^{b}})}^{2}}={{3}^{a}}.\ {{3}^{c}}\ i.e.\ {{3}^{a}},\ {{3}^{b}},\ {{3}^{c}}\] are in G.P. Note: Students should remember this question as a fact.


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