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MathNet 2016-part-05 — 184 problems (EN–VI) Question 73

Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)

Question 73

The sum of every three consecutive terms of the sequence $a_1, a_2, a_3, a_4, \dots$ equals $2016$. It also holds that $a_{667} = 667$ and $a_{1004} = 1004$. What is the value of $a_{2016}$?
(A) 0
(B) 345
(C) 667
(D) 1004
(E) 2016