Question
What is the average of the squares of the first 31 natural
numbers?Solution
Sum of squares of first 'n' natural numbers = n Ă— (n + 1) Ă— (2n + 1) Ă· 6
So, average = n Ă— (n + 1) Ă— (2n + 1) Ă· 6n = (n + 1) Ă— (2n + 1) Ă· 6
= (31 + 1) Ă— (2 Ă— 31 + 1) Ă· 6
= 32 Ă— 63 Ă· 6
= 336
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