JEE Main & Advanced Mathematics Sequence & Series Question Bank Arithmetic Progression

  • question_answer
    If \[a,\,b,\,c\] are in A.P., then \[(a+2b-c)\]\[(2b+c-a)\]\[(c+a-b)\]  equals [Pb. CET 1999]

    A) \[\frac{1}{2}abc\]

    B) abc

    C) 2 abc

    D) 4 abc

    Correct Answer: D

    Solution :

    \[(a+2b-c)\,(2b+c-a)\,(c+a-b)\] \[=(a+a+c-c)(a+c+c-a)(2b-b)\]\[=4\,abc.\] \[(\because a,b,c\] are in A.P., \[\therefore 2b=a+c)\].


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