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

  • question_answer
    If sum of \[n\] terms of an A.P. is \[3{{n}^{2}}+5n\] and \[{{T}_{m}}=164\] then \[m=\]           [RPET 1991, 95; DCE 1999]

    A) 26

    B) 27

    C) 28

    D) None of these

    Correct Answer: B

    Solution :

    Obviously \[164=(3{{m}^{2}}+5m)-\{3{{(m-1)}^{2}}+5(m-1)\}\] \[=(3{{m}^{2}}+5m)-3{{m}^{2}}+6m-3-5m+5\] \[\Rightarrow \]\[164=6m+2\]\[\Rightarrow \]\[m=27\].


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