What is the average of the squares of the first 46 natural numbers?

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Accepted Answer

To find the average of the squares of the first 46 natural numbers, we use the formula for the sum of squares of first n natural numbers:

Sum of squares = n(n + 1)(2n + 1) / 6

For n = 46:
Sum = 46 × 47 × 93 / 6

Calculate step-by-step:
46 × 47 = 2162
2162 × 93 = 201066
201066 / 6 = 33511

Now, average = Sum / n = 33511 / 46 ≈ 728.5

Hence, the average of the squares of the first 46 natural numbers is 728.5.

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