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MATH / The sequence a₀, a₁, a₂, … satisfies the recurrence equation

Problem

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problem

The sequence a0a_0, a1a_1, a2a_2, …\ldots\, satisfies the recurrence equation an=2an−1−2an−2+an−3 a_n = 2 a_{n-1} - 2 a_{n - 2} + a_{n - 3} for every integer n≥3n \ge 3. If a20=1a_{20} = 1, a25=10a_{25} = 10, and a30=100a_{30} = 100, what is the value of a1331a_{1331}?
Plain-text mathematical notation (without MathML)
The sequence a₀, a₁, a₂, …  satisfies the recurrence equation
a_(n)=2a_(n−1)−2a_(n−2)+a_(n−3)for every integer n≥3.  If a₂₀=1, a₂₅=10, and a₃₀=100, what is the value of a₁₃₃₁?
Original LaTeX notation
The sequence $a_0$, $a_1$, $a_2$, $\ldots\,$ satisfies the recurrence equation
\[
  a_n = 2 a_{n-1} - 2 a_{n - 2} + a_{n - 3}
\]for every integer $n \ge 3$.  If $a_{20} = 1$, $a_{25} = 10$, and $a_{30} = 100$, what is the value of $a_{1331}$?

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
0ed1d6e9-7fa7-5c08-99a3-237da6551ebd
task_key
intermediate~5falgebra--test--0ed1d6e9-7fa7-5c08-99a3-237da6551ebd
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import