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    The average of the first 30 natural numbers is:
    Question

    The average of the first 30 natural numbers is:

    A.

    15

    B.

    16

    C.

    15.5

    D.

    16.5

    Correct option is C

    Given:

    First 30 natural numbers.

    Formula Used:

    Average=Sum of numbersCount of numbers\text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}}

    Sum of first n natural numbers=n(n+1)2\text{Sum of first $ n $ natural numbers} = \frac{n(n+1)}{2}​​

    Solution: 

    Now, 

    Sum=30×(30+1)2=30×312=465\text{Sum} = \frac{30 \times (30 + 1)}{2} = \frac{30 \times 31}{2} = 465 

    Thus , 

    Average=46530=15.5\text{Average} = \frac{465}{30} = 15.5 ​​

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