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Find the average of 12 + 22 + 32 + 42 + ...... 102.
1. 46
2. 38.5
3. 86
4. 49

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Correct Answer - Option 2 : 38.5

Formula used:

The average of squares of first n natural numbers = [(n + 1)(2n + 1)]/6

Calculation:

Average = [(n + 1)(2n + 1)]/6

⇒ Average = [(10 + 1)(2 × 10 + 1)]/6

⇒ Average = (11 × 21)/6 = 231/6 

⇒ Average = 231/6 = 38.5

∴ The average of 12 + 22 + 32 + 42 + ...... 10is 38.5.

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