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Omni-MATH / Let a₀,a₁,a₂,… be a sequence of real numbers defined by a₀=21,a₁=35, and a_(n+2)=4a_(n+1)−4a_(n)+n² for n≥2. Compute the remainder obtained when a₂₀₀₆ is divided by 100.

Problem

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problem

Let a0,a1,a2,…a_{0}, a_{1}, a_{2}, \ldots be a sequence of real numbers defined by a0=21,a1=35a_{0}=21, a_{1}=35, and an+2=4an+1−4an+n2a_{n+2}=4 a_{n+1}-4 a_{n}+n^{2} for n≥2n \geq 2. Compute the remainder obtained when a2006a_{2006} is divided by 100.
Plain-text mathematical notation (without MathML)
Let a₀,a₁,a₂,… be a sequence of real numbers defined by a₀=21,a₁=35, and a_(n+2)=4a_(n+1)−4a_(n)+n² for n≥2. Compute the remainder obtained when a₂₀₀₆ is divided by 100.
Original LaTeX notation
Let $a_{0}, a_{1}, a_{2}, \ldots$ be a sequence of real numbers defined by $a_{0}=21, a_{1}=35$, and $a_{n+2}=4 a_{n+1}-4 a_{n}+n^{2}$ for $n \geq 2$. Compute the remainder obtained when $a_{2006}$ is divided by 100.

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Source and history

task_id
68b74f3f-9e20-576b-b33d-a43de918ef31
task_key
test--68b74f3f-9e20-576b-b33d-a43de918ef31
task_revision_id
1
config / split
/ test

Official source

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