{"status": "success", "data": {"description_md": "Let $a_1 , a_2 , ...$ be a sequence for which\n$a_1=2$ , $a_2=3$, and $a_n=\\frac{a_{n-1}}{a_{n-2}}$ for each positive integer $n \\ge 3$. \nWhat is $a_{2006}$?\n\n$\\mathrm{(A) \\ } \\frac{1}{2}\\qquad \\mathrm{(B) \\ } \\frac{2}{3}\\qquad \\mathrm{(C) \\ } \\frac{3}{2}\\qquad \\mathrm{(D) \\ } 2\\qquad \\mathrm{(E) \\ } 3$", "description_html": "<p>Let  <span class=\"katex--inline\">a_1 , a_2 , ...</span>  be a sequence for which<br/>\n <span class=\"katex--inline\">a_1=2</span>  ,  <span class=\"katex--inline\">a_2=3</span> , and  <span class=\"katex--inline\">a_n=\\frac{a_{n-1}}{a_{n-2}}</span>  for each positive integer  <span class=\"katex--inline\">n \\ge 3</span> .<br/>\nWhat is  <span class=\"katex--inline\">a_{2006}</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{1}{2}\\qquad \\mathrm{(B) \\ } \\frac{2}{3}\\qquad \\mathrm{(C) \\ } \\frac{3}{2}\\qquad \\mathrm{(D) \\ } 2\\qquad \\mathrm{(E) \\ } 3</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": 3, "problem_name": "2006 AMC 10B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc10B_p19", "prev": "/problem/06_amc10B_p17"}}