Question
Download Solution PDFWhat is the sum of the squares of the numbers from 3 to 18?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
Last updated on Jul 1, 2025
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