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

  • question_answer
    The sum of all natural numbers between 1 and 100 which are multiples of 3 is [MP PET 1984]

    A) 1680

    B) 1683

    C) 1681

    D) 1682

    Correct Answer: B

    Solution :

    We get series 3, 6, 9, 12,........ 99. Here\[n=\frac{99}{3}=33,\ a=3,\ d=3\], therefore \[S=\frac{33}{2}\left\{ 2\times 3+(33-1)3 \right\}\]    \[=\frac{33}{2}\times 102=33\times 51=1683\].


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