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2023 AMC 10BProblem 6P1-10~2 minPrint
Modular ArithmeticSequences & SeriesUse an invariant, parity, or coloring argumentCompute small cases, spot the pattern, generalize

Let L1=1L_1 = 1 , L2=3L_2 = 3 , and Ln+2=Ln+1+LnL_{n+2} = L_{n+1}+L_n for n≥1n \geq 1 . How many terms in the sequence L1,L2,L3,⋯ ,L2023L_1, L_2, L_3, \cdots, L_{2023} are even?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.