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Recursive Sequence

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January 6, 2009

Problem Statement

In the sequence 2001,2002,2003,… 2001, 2002, 2003, \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 \plus{} 2002 \minus{} 2003 \equal{} 2000. What is the 2004th 2004^\text{th} term in this sequence? (A) \minus{} \! 2004 \qquad (B) \minus{} \! 2 \qquad (C)\ 0 \qquad (D)\ 4003 \qquad (E)\ 6007
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