Given that (1² + 2² + 3² + .......... + 10²) = 385, then the value of (2² + 4² + 6² + .......... + 20²) is equal to = ?

Question: Given that (1² + 2² + 3² + .......... + 10²) = 385, then the value of (2² + 4² + 6² + .......... + 20²) is equal to = ?

Solution:
(2² + 4² + 6² + .......... + 20²)
= (1 × 2)² + (2 × 2)² + (3 × 2)² + ............. + (2 × 10)²
= (1² × 2²) + (2² × 2²) + (3² × 2²) ............ + (2² × 10²)
= 2²(1² + 2² + 3² + .......... + 10²)
= 4 × 385 [Putting the value (1² + 2² + 3² + .......... + 10²) = 385]
= 1540