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2017 AMC 10A Problems/Problem 13: Difference between revisions

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Created page with "Define a sequence recursively by <math>F_{0}=0,~F_{1}=1,</math> and <math>F_{n}=</math> the remainder when <math>F_{n-1}+F_{n-2}</math> is divided by <math>3,</math> for all <..."
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Revision as of 15:49, 8 February 2017

Define a sequence recursively by $F_{0}=0,~F_{1}=1,$ and $F_{n}=$ the remainder when $F_{n-1}+F_{n-2}$ is divided by $3,$ for all $n\geq 2.$ Thus the sequence starts $0,1,1,2,0,2,\ldots$ What is $F_{2017}+F_{2018}+F_{2019}+F_{2020}+F_{2021}+F_{2022}+F_{2023}+F_{2024}?$

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