The value of 5² + 6² + .... + 10² + 20² is :

Solution (By Examveda Team)

= 5² + 6² + .... + 10² + 20²
= (1² + 2² + 3² +..... + 10²) - (1² + 2² + 3² + 4²) + 400
= $$\frac{1}{6}$$ n(n + 1) (2n + 1) - (1 + 4 + 9 + 16) + 400, where n = 10
= $$\left( {\frac{1}{6} \times 10 \times 11 \times 21} \right)$$     - 30 + 400
= (385 - 30 + 400)
= 755