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Problem 486

AMC 12 late, AIME early

Algebra Difficulty 4.9 Find the answer

Problem 9-1. Calculate the sum $1^{2}+2^{2}-3^{2}-4^{2}+5^{2}+6^{2}-7^{2}-8^{2}+9^{2}+10^{2}-\ldots+2017^{2}+2018^{2}$ .

Your answer

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

Answer: 4074341.

Solution. Note that for any $k$ the equality $k^{2}-(k+1)^{2}-(k+2)^{2}+(k+3)^{2}=4$ holds. Therefore, the entire sum is equal to $1+504 \cdot 4+2018^{2}=4074341$ .

Rating	Score	Content of the criterion
+	20	Complete solution
$+/-$	16	Correct solution with an arithmetic error
$-/+$	8	Correct idea of the solution with completely incorrect calculation and answer
-	0	Solution is completely incorrect/only answer

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.