(22 + 42 + 62 + … + 202) = ?

Question:
(22 + 42 + 62 + … + 202) = ?

[A].

770

[B].

1155

[C].

1540

[D].

385 x 385

Answer: Option C

Explanation:

(22 + 42 + 62 + … + 202) = (1 x 2)2 + (2 x 2)2 + (2 x 3)2 + … + (2 x 10)2

= (22 x 12) + (22 x 22) + (22 x 32) + … + (22 x 102)

= 22 x [12 + 22 + 32 + … + 102]

	Ref: (12 + 22 + 32 + … + n2) =	1	n(n + 1)(2n + 1)
		6

=		4 x	1	x 10 x 11 x 21
			6

= (4 x 5 x 77)

= 1540.