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

  • question_answer
    If \[\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}(x\ne 0)\], then \[a,\ b,\ c,\ d\] are in [RPET 1986]

    A) A.P.

    B) G.P.

    C) H.P.

    D) None of these

    Correct Answer: B

    Solution :

    \[\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}\] Applying componendo and dividendo, we get \[\frac{2a}{2bx}=\frac{2b}{2cx}=\frac{2c}{2dx}\]\[\Rightarrow \]\[{{b}^{2}}=ac\] and  \[{{c}^{2}}=bd\] \[\Rightarrow \]\[a,\ b,\ c\]and \[b,\ c,\ d\]  are in G.P. Therefore, \[a,\ b,\ c,\ d\] are in G.P.


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