Difference between revisions of "2019 AMC 12B Problems/Problem 22"

Revision as of 16:39, 14 February 2019

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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

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 In which of the following intervals does <math>m</math> lie?
+<math>\textbf{(A) }[9,26]\qquad\textbf{(B) }[27,80]\qquad\textbf{(C) }[81,242]\qquad\textbf{(D) }[243,728]\qquad\textbf{(E) }[729,\infty)</math>
 ==Solution==