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Turkish NMO First Round - 2000 P-12 (Algebra)

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July 7, 2012

Problem Statement

(an)(a_n) is a sequence with a1=1a_1=1 and ∣an∣=∣an−1+2∣|a_n| = |a_{n-1}+2| for every positive integer n≥2n\geq 2. What is the minimum possible value of ∑i=12000ai\sum_{i = 1}^{2000}a_{i}?
<spanclass=′latex−bold′>(A)</span> −4000<spanclass=′latex−bold′>(B)</span> −3000<spanclass=′latex−bold′>(C)</span> −2000<spanclass=′latex−bold′>(D)</span> −1000<spanclass=′latex−bold′>(E)</span> None <span class='latex-bold'>(A)</span>\ -4000 \qquad<span class='latex-bold'>(B)</span>\ -3000 \qquad<span class='latex-bold'>(C)</span>\ -2000 \qquad<span class='latex-bold'>(D)</span>\ -1000 \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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