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Omni-MATH / The sequence a₁,a₂,a₃,… of real numbers satisfies the recurrence a_(n+1)=(a_(n)²−a_(n−1)+2a_(n))/(a_(n−1)+1). Given that a₁=1 and a₉=7, find a₅.

Problem

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problem

The sequence a1,a2,a3,…a_{1}, a_{2}, a_{3}, \ldots of real numbers satisfies the recurrence an+1=an2−an−1+2anan−1+1a_{n+1}=\frac{a_{n}^{2}-a_{n-1}+2 a_{n}}{a_{n-1}+1}. Given that a1=1a_{1}=1 and a9=7a_{9}=7, find a5a_{5}.
Plain-text mathematical notation (without MathML)
The sequence a₁,a₂,a₃,… of real numbers satisfies the recurrence a_(n+1)=(a_(n)²−a_(n−1)+2a_(n))/(a_(n−1)+1). Given that a₁=1 and a₉=7, find a₅.
Original LaTeX notation
The sequence $a_{1}, a_{2}, a_{3}, \ldots$ of real numbers satisfies the recurrence $a_{n+1}=\frac{a_{n}^{2}-a_{n-1}+2 a_{n}}{a_{n-1}+1}$. Given that $a_{1}=1$ and $a_{9}=7$, find $a_{5}$.

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Source and history

task_id
f8416469-bdea-555c-ac3d-68aebcd9b979
task_key
test--f8416469-bdea-555c-ac3d-68aebcd9b979
task_revision_id
1
config / split
/ test

Official source

initial import