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

  • question_answer
    The \[{{n}^{th}}\] term of an A.P. is \[3n-1\].Choose from the following the sum of its first five terms [MP PET 1983]

    A) 14

    B) 35

    C) 80

    D) 40

    Correct Answer: D

    Solution :

    Here\[{{T}_{n}}=3n-1\], putting \[n=1,\ 2,\ 3,\ 4,\ 5\] we get first five terms, \[2,\ 5,\ 8,\ 11,\ 14\] Hence sum is\[{{n}^{th}}\]. Aliter: \[{{S}_{n}}=\Sigma {{T}_{n}}=3\Sigma n-\Sigma 1=\frac{3n(n+1)}{2}-n\] \[\Rightarrow \] \[{{S}_{5}}=\frac{3.5.6}{2}-5=40\].


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