What is the sum of the squares of the numbers from 3 to 18?

Given:

We need to find the sum of squares from 3 to 18

Formula used:

Sum of squares from 1 to n = \(\dfrac{n(n+1)(2n+1)}{6}\)

Sum of squares from a to b = Sum of squares from 1 to b − Sum of squares from 1 to (a−1)

Calculation:

Sum = \(\dfrac{18(18+1)(2×18+1)}{6} - \dfrac{2(2+1)(2×2+1)}{6}\)

⇒ Sum = \(\dfrac{18×19×37}{6} - \dfrac{2×3×5}{6}\)

⇒ Sum = \(\dfrac{12654}{6} - \dfrac{30}{6}\)

⇒ Sum = 2109 - 5

⇒ Sum = 2104

∴ The correct answer is 2104.