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MATH / Define a sequence recursively by F_{0}=0,~F_{1}=1, and F_(n) be the remainder when F_(n−1)+F_(n−2) is divided by 3, for all n≥2. Thus the sequence starts 0,1,1,2,0,2,… What is …

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problem

Define a sequence recursively by $F_{0}=0,~F_{1}=1,$ and FnF_{n} be the remainder when Fn−1+Fn−2F_{n-1}+F_{n-2} is divided by 3,3, for all n≥2.n\geq 2. Thus the sequence starts 0,1,1,2,0,2,…0,1,1,2,0,2,\ldots What is $F_{2017}+F_{2018}+F_{2019}+F_{2020}+F_{2021}+F_{2022}+F_{2023}+F_{2024}?$
Plain-text mathematical notation (without MathML)
Define a sequence recursively by $F_{0}=0,~F_{1}=1,$ and F_(n) be the remainder when F_(n−1)+F_(n−2) is divided by 3, for all n≥2. Thus the sequence starts 0,1,1,2,0,2,… What is $F_{2017}+F_{2018}+F_{2019}+F_{2020}+F_{2021}+F_{2022}+F_{2023}+F_{2024}?$
Original LaTeX notation
Define a sequence recursively by $F_{0}=0,~F_{1}=1,$ and $F_{n}$ be 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 $F_{2017}+F_{2018}+F_{2019}+F_{2020}+F_{2021}+F_{2022}+F_{2023}+F_{2024}?$

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
a223590b-f9fc-5b0f-a165-f84bd99dc514
task_key
intermediate~5falgebra--test--a223590b-f9fc-5b0f-a165-f84bd99dc514
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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