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MathNet 2016-part-05 — 184 problems (EN–VI) Question 69

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

Question 69

In the sequence $a_{1}, a_{2}, a_{3}, a_{4}, \ldots$ the sum of every three consecutive terms equals 2016. It also holds that $a_{667}=667$ and $a_{1004}=1004$. What is $a_{2016}$?

(A) 0
(B) 345
(C) 667
(D) 1004
(E) 2016