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

  • question_answer
    If \[a,\ b,\ c\], d are any four consecutive coefficients of  any expanded binomial, then \[\frac{a+b}{a},\ \frac{b+c}{b},\ \frac{c+d}{c}\] are in

    A) A.P.

    B) G.P.

    C) H.P.

    D) None of the above

    Correct Answer: C

    Solution :

    Let \[a={}^{n}{{C}_{r-1}},\ b={}^{n}{{C}_{r}},\,C={}^{n}{{c}_{r+1}}\] and\[d={}^{n}{{c}_{r+2}}\]. Substituting these values in problem, we get \[\frac{a+b}{a},\ \frac{b+c}{b},\ \frac{c+d}{c}\] are in H.P.


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