olymmath

AIME 2006a Problem 15

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Given that a sequence of real numbers satisfies x0=0x_0=0 and ∣xk∣=∣xk−1+3∣|x_k|=|x_{k-1}+3| for all integers k≥1,k\ge 1, find the minimum possible value of ∣x1+x2+⋯+x2006∣.|x_1+x_2+\cdots+x_{2006}|.

Dataset text AIME 1983 to 2026. Quoted with source.

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