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Question : $\small \left ( 5^{2}+6^{2}+7^{2}+.....+10^{2} \right )$ is equal to:
Option 1: 330
Option 2: 345
Option 3: 355
Option 4: 360

Team Careers360 9th Jan, 2024

Answer (1)

Team Careers360 12th Jan, 2024

Correct Answer: 355

Solution : We know that $1^{2}+2^{2}+3^{2}+.....+n^{2}=\frac{n(n+1)(2n+1)}{6}$
So, $1^{2}+2^{2}+3^{2}+.....+10^{2}=\frac{10(10+1)(2\times 10+1)}{6}$-----------------(1)
Also, $1^{2}+2^{2}+.....+4^{2}=\frac{4(4+1)(2\times 4+1)}{6}$------------------------------(2)
Subtracting equation (2) from (1), we get,
$5^{2}+6^{2}+.....+10^{2}=\frac{10(10+1)(2\times 10+1)}{6}-\frac{4(4+1)(2\times 4+1)}{6}$
$\therefore5^{2}+6^{2}+.....+10^{2}=355$
Hence, the correct answer is 355.

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