What is the average of the squares of the first 48 natural numbers?

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Accepted Answer

Step 1: The formula for the sum of squares of first n natural numbers is n(n+1)(2n+1)/6.

Step 2: For n = 48, calculate the sum of squares:
Sum = 48 × 49 × 97 / 6

Step 3: Calculate numerator:
48 × 49 = 2352
2352 × 97 = 228144

Step 4: Divide by 6:
228144 / 6 = 38024

Step 5: Average = Sum of squares / number of terms = 38024 / 48 = 792.1666...

Step 6: Rounded to two decimal places, the average is 792.17.

Therefore, the correct answer is 792.17.

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