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    The average of the squares of the first 83 natural numbers is
    Question

    The average of the squares of the first 83 natural numbers is

    A.

    2337

    B.

    2340

    C.

    2338

    D.

    2339

    Correct option is C

    Given:
    n = 83
    Formula Used:
    Average of squares of first n natural numbers = (n+1)(2n+1)6\frac{(n+1)(2n+1)}{6}​​
    Solution:
    Average=(83+1)(2×83+1)6 Average=84×1676 Average=14×167=2338\text{Average} = \frac{(83 + 1)(2 \times 83 + 1)}{6}\\ \ \\\text{Average} = \frac{84 \times 167}{6}\\ \ \\\text{Average} = 14 \times 167 = 2338​​
    So the correct answer is (c).

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