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MATH / Let a₀=2, a₁=5, and a₂=8, and for n>2 define a_(n) recursively to be the remainder when 4(a_(n−1)+a_(n−2)+a_(n−3)) is divided by 11. Find a₂₀₁₈⋅a₂₀₂₀⋅a₂₀₂₂.

Problem

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problem

Let a0=2a_{0} = 2, a1=5a_{1} = 5, and a2=8a_{2} = 8, and for n>2n > 2 define ana_{n} recursively to be the remainder when 4(an−1+an−2+an−3)4(a_{n-1} + a_{n-2} + a_{n-3}) is divided by 1111. Find a2018⋅a2020⋅a2022a_{2018} \cdot a_{2020} \cdot a_{2022}.
Plain-text mathematical notation (without MathML)
Let a₀=2, a₁=5, and a₂=8, and for n>2 define a_(n) recursively to be the remainder when 4(a_(n−1)+a_(n−2)+a_(n−3)) is divided by 11. Find a₂₀₁₈⋅a₂₀₂₀⋅a₂₀₂₂.
Original LaTeX notation
Let $a_{0} = 2$, $a_{1} = 5$, and $a_{2} = 8$, and for $n > 2$ define $a_{n}$ recursively to be the remainder when $4(a_{n-1} + a_{n-2} + a_{n-3})$ is divided by $11$. Find $a_{2018} \cdot a_{2020} \cdot a_{2022}$.

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
8952e7b0-8dc6-58f9-bd72-cca746a2338e
task_key
intermediate~5falgebra--test--8952e7b0-8dc6-58f9-bd72-cca746a2338e
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import