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Recursive Sequence

Source: AMC 10 2008B Problem 11

March 1, 2008
AMC

Problem Statement

Suppose that (un) \left(u_n\right) is a sequence of real numbers satisfying u_{n \plus{} 2} \equal{} 2u_{n \plus{} 1} \plus{} u_{n}, and that u_3 \equal{} 9 and u_6 \equal{} 128. What is u5 u_5? <spanclass=′latex−bold′>(A)</span> 40<spanclass=′latex−bold′>(B)</span> 53<spanclass=′latex−bold′>(C)</span> 68<spanclass=′latex−bold′>(D)</span> 88<spanclass=′latex−bold′>(E)</span> 104 <span class='latex-bold'>(A)</span>\ 40 \qquad <span class='latex-bold'>(B)</span>\ 53 \qquad <span class='latex-bold'>(C)</span>\ 68 \qquad <span class='latex-bold'>(D)</span>\ 88 \qquad <span class='latex-bold'>(E)</span>\ 104
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