{"status": "success", "data": {"description_md": "Define a sequence recursively by $x_0=5$ and\n$$x_{n+1}=\\frac{x_n^2+5x_n+4}{x_n+6}$$for all nonnegative integers $n.$ Let $m$ be the least positive integer such that\n$$x_m\\leq 4+\\frac{1}{2^{20}}.$$In which of the following intervals does $m$ lie?\n\n$\\textbf{(A) } [9,26] \\qquad\\textbf{(B) } [27,80] \\qquad\\textbf{(C) } [81,242]\\qquad\\textbf{(D) } [243,728] \\qquad\\textbf{(E) } [729,\\infty)$", "description_html": "<p>Define a sequence recursively by  <span class=\"katex--inline\">x_0=5</span>  and<br/>\n <span class=\"katex--display\">x_{n+1}=\\frac{x_n^2+5x_n+4}{x_n+6}</span> for all nonnegative integers  <span class=\"katex--inline\">n.</span>  Let  <span class=\"katex--inline\">m</span>  be the least positive integer such that<br/>\n <span class=\"katex--display\">x_m\\leq 4+\\frac{1}{2^{20}}.</span> In which of the following intervals does  <span class=\"katex--inline\">m</span>  lie?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } [9,26] \\qquad\\textbf{(B) } [27,80] \\qquad\\textbf{(C) } [81,242]\\qquad\\textbf{(D) } [243,728] \\qquad\\textbf{(E) } [729,\\infty)</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2019 AMC 10B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10B_p25", "prev": "/problem/19_amc10B_p23"}}