AMC 10 Step by Step
2004 AMC 10BProblem 19P16-20~4 minPrint

In the sequence 20012001 , 20022002 , 20032003 , \ldots , each term after the third is found by subtracting the previous term from the sum of the two terms that precede that term. For example, the fourth term is 2001+20022003=20002001 + 2002 - 2003 = 2000 . What is the 2004th2004^\textrm{th} term in this sequence?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2004 12B #12.