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

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OSSC Junior Stenographer, Junior Typist (Prelims) Official Paper (Held On: 09 Feb, 2025)
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  1. 2104
  2. 2105
  3. 2101
  4. 2106

Answer (Detailed Solution Below)

Option 1 : 2104
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Detailed Solution

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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.

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