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Omni-MATH / Let a₁=3, and for n>1, let a_(n) be the largest real number such that 4(a_(n−1)²+a_(n)²)=10a_(n−1)a_(n)−9 What is the largest positive integer less than a₈ ?

Problem

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problem

Let a1=3a_{1}=3, and for n>1n>1, let ana_{n} be the largest real number such that 4(an−12+an2)=10an−1an−94\left(a_{n-1}^{2}+a_{n}^{2}\right)=10 a_{n-1} a_{n}-9 What is the largest positive integer less than a8a_{8} ?
Plain-text mathematical notation (without MathML)
Let a₁=3, and for n>1, let a_(n) be the largest real number such that 4(a_(n−1)²+a_(n)²)=10a_(n−1)a_(n)−9 What is the largest positive integer less than a₈ ?
Original LaTeX notation
Let $a_{1}=3$, and for $n>1$, let $a_{n}$ be the largest real number such that $$4\left(a_{n-1}^{2}+a_{n}^{2}\right)=10 a_{n-1} a_{n}-9$$ What is the largest positive integer less than $a_{8}$ ?

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Source and history

task_id
fc2db080-2af7-5332-b05d-6205ac466341
task_key
test--fc2db080-2af7-5332-b05d-6205ac466341
task_revision_id
1
config / split
/ test

Official source

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