2019 AMC 12B Problems/Problem 22

Problem

Define a sequence recursively by $x_0 = 5$ and

$x_{n+1} = \frac{x_n^2 + 5x_n + 4}{x_n + 6}$

for all nonnegative integers $n$ . Let $m$ be the least positive integer such that $x_m \leq 4 + \frac{1}{2^{20}}$ .

In which of the following intervals does $m$ lie?

$\textbf{(A) }[9,26]\qquad\textbf{(B) }[27,80]\qquad\textbf{(C) }[81,242]\qquad\textbf{(D) }[243,728]\qquad\textbf{(E) }[729,\infty)$

2019 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 21	Followed by Problem 23
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