What is the average of the squares of the first 47 natural numbers?

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Accepted Answer

To find the average of the squares of the first 47 natural numbers, we use the formula for the sum of squares of first n natural numbers:

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

For n = 47:
Sum = 47 × 48 × 95 / 6

Calculate step-by-step:
47 × 48 = 2256
2256 × 95 = 214320
Divide by 6: 214320 / 6 = 35720

So, sum of squares = 35720

Average = Sum / n = 35720 / 47 = 760

Therefore, the average of the squares of the first 47 natural numbers is 760.

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