Question
What is the average of the squares of the first 29 natural numbers?
Solution
Sum of squares of first 'n' natural numbers = n × (n + 1) × (2n + 1) ÷ 6
So, average = n × (n + 1) × (2n + 1) ÷ 6n = (n + 1) × (2n + 1) ÷ 6
= (29 + 1) × (2 × 29 + 1) ÷ 6
= 30 × 59 ÷ 6
= 295
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