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Turkey NMO 2008 1st Round - P11 (Algebra)

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August 25, 2012

Problem Statement

Sequence (an)(a_n) is defined as an+1−2an+an−1=7a_{n+1}-2a_n+a_{n-1}=7 for every n≥2n\geq 2, where a1=1,a2=5a_1 = 1, a_2=5. What is a17a_{17}?
<spanclass=′latex−bold′>(A)</span> 895<spanclass=′latex−bold′>(B)</span> 900<spanclass=′latex−bold′>(C)</span> 905<spanclass=′latex−bold′>(D)</span> 910<spanclass=′latex−bold′>(E)</span> None of the above <span class='latex-bold'>(A)</span>\ 895 \qquad<span class='latex-bold'>(B)</span>\ 900 \qquad<span class='latex-bold'>(C)</span>\ 905 \qquad<span class='latex-bold'>(D)</span>\ 910 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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