Printable

2019 AMC 10B Problem 24

Include the solution Back to the problem

2019 AMC 10B Problem 24AMC 10 Step by Step

Name: Date: September 13, 2026

Sequences & Series · difficulty 5 of 5 · about 10 min · position P21-25

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?

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

2019 AMC 10B Problem 24

Working