Question
What is the average of the squares of the first 17 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
= (17 + 1) Ă— (2 Ă— 17 + 1) Ă· 6
= 18 Ă— 35 Ă· 6
= 105
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