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HMMT 2001 U47

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For the sequence of numbers n1,n2,n3,…n_{1}, n_{2}, n_{3}, \ldots, the relation ni=2ni−1+an_{i}=2 n_{i-1}+a holds for all i>1i>1. If n2=5n_{2}=5 and n8=257n_{8}=257, what is n5n_{5} ?

Dataset text NuminaMath olympiads. Quoted with source.

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