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    What is the average of the squares of first 14 natural numbers?
    Question

    What is the average of the squares of first 14 natural numbers?

    A.

    76.5

    B.

    74

    C.

    72.5

    D.

    78

    Correct option is C

    Given:
    First 14 natural numbers.
    Formula Used:
    Average of squares of first n natural numbers = (n+1)(2n+1)6 \frac{(n + 1)(2n + 1)}{6}​​
    Solution:
    Here, n = 14.
    Substitute the value of n in the formula.
    Average = (14+1)(2×14+1)6 \frac{(14 + 1)(2 × 14 + 1)}{6}​​
    =15×(28+1)6 = \frac{15 × (28 + 1)}{6}​​

    =15×296 = \frac{15 × 29}{6}​​

    = 72.5
    Final Answer
    So the correct answer is (c)

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