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MATH / Let a sequence be defined as follows: a₁=3, a₂=3, and for n≥2,

Problem

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problem

Let a sequence be defined as follows: a1=3,a_1 = 3, a2=3,a_2 = 3, and for n≥2,n \ge 2, an+1an−1=an2+2007.a_{n + 1} a_{n - 1} = a_n^2 + 2007.Find the largest integer less than or equal to a20072+a20062a2007a2006\frac{a_{2007}^2+a_{2006}^2}{a_{2007}a_{2006}}.
Plain-text mathematical notation (without MathML)
Let a sequence be defined as follows: a₁=3, a₂=3, and for n≥2,
a_(n+1)a_(n−1)=a_(n)²+2007.Find the largest integer less than or equal to (a₂₀₀₇²+a₂₀₀₆²)/(a₂₀₀₇a₂₀₀₆).
Original LaTeX notation
Let a sequence be defined as follows: $a_1 = 3,$ $a_2 = 3,$ and for $n \ge 2,$
\[a_{n + 1} a_{n - 1} = a_n^2 + 2007.\]Find the largest integer less than or equal to $\frac{a_{2007}^2+a_{2006}^2}{a_{2007}a_{2006}}$.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
c9c1fb7b-6cc0-5d3f-995f-d65adaa4c756
task_key
intermediate~5falgebra--test--c9c1fb7b-6cc0-5d3f-995f-d65adaa4c756
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import