SSC CGL 2024 PYQ — Question 60

The correct answer is option 2 i.e. 728.5.

The sum of the squares of the first n natural numbers = ${n(n + 1)(2n + 1)\over 6}$

Sum of numbers = Average of numbers × Number of numbers

According to the given question,

Sum of first 46 natural numbers = ${46(46 + 1)(2(46) + 1)\over 6}$

⇒ ${46 \times 47 \times 93\over 6}$ 

⇒ 23 × 47 ×31 = 33511

Average = $33511 \over 46$

⇒ 728.5

Hence the average of the squares of the first 46 natural numbers is 728.5.