Discussion

If \(1^2 + 2^2 + 3^2 + ... + 10^2 = 385\), then the value of \(2^2 + 4^2 + 6^2 + ... + 20^2\) is:

Answer: C

Let the required sum be S.

\(S = 2^2 + 4^2 + 6^2 + ... + 20^2\).

\(S = (2 \times 1)^2 + (2 \times 2)^2 + (2 \times 3)^2 + ... + (2 \times 10)^2\).

\(S = 2^2(1^2) + 2^2(2^2) + 2^2(3^2) + ... + 2^2(10^2)\).

\(S = 2^2 (1^2 + 2^2 + 3^2 + ... + 10^2)\).

\(S = 4 \times (\text{given sum})\).

\(S = 4 \times 385 = 1540\).

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