AIME 2009 II #14 — a₀=0 a_{n+1}=8/5·aₙ+6/5·√(4ⁿ-aₙ²)

2550MasterTrigonometryAlgebraSequences & Series

AIME II · 2009 · Problem 14

The sequence $(a_n)$ satisfies $a_0=0$ and $a_{n + 1} = \frac{8}{5}a_n + \frac{6}{5}\sqrt{4^n - a_n^2}$ for $n \geq 0$. Find the greatest integer less than or equal to $a_{10}$.

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AIME 2009 II #14 — a₀=0 a_{n+1}=8/5·aₙ+6/5·√(4ⁿ-aₙ²)

2550MasterTrigonometryAlgebraSequences & Series

AIME II · 2009 · Problem 14

The sequence $(a_n)$ satisfies $a_0=0$ and $a_{n + 1} = \frac{8}{5}a_n + \frac{6}{5}\sqrt{4^n - a_n^2}$ for $n \geq 0$. Find the greatest integer less than or equal to $a_{10}$.

0 students attempted0% solvedRating 2550