$15^{2} + 20^{2} + 25^{2} + . . . + 100^{2} =$

71220

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71625

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71750

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71800

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Solution

The correct option is B 71625
$S = 15^{2} + 20^{2} + 25^{2} + . . . + 100^{2} = 5^{2} (3^{2} + 4^{2} + 5^{2} + . . . + 20^{2})$
Now, $3^{2} + 4^{2} + 5^{2} + . . . + 20^{2} = (1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + . . . + 20^{2}) - (1^{2} + 2^{2}) = [\frac{20 (20 + 1) (2 (20) + 1)}{6}] - 5 = \frac{17220}{6} - 5 = 2865$

$\Rightarrow S = 25 \times 2865 = 71625$

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