{"status": "success", "data": {"description_md": "Let $\\{a_k\\}$ be a sequence of integers such that $a_1=1$ and $a_{m+n}=a_m+a_n+mn,$ for all positive integers $m$ and $n.$ Then $a_{12}$ is\n\n$\\mathrm{(A) \\ } 45\\qquad \\mathrm{(B) \\ } 56\\qquad \\mathrm{(C) \\ } 67\\qquad \\mathrm{(D) \\ } 78\\qquad \\mathrm{(E) \\ } 89$", "description_html": "<p>Let  <span class=\"katex--inline\">\\{a_k\\}</span>  be a sequence of integers such that  <span class=\"katex--inline\">a_1=1</span>  and  <span class=\"katex--inline\">a_{m+n}=a_m+a_n+mn,</span>  for all positive integers  <span class=\"katex--inline\">m</span>  and  <span class=\"katex--inline\">n.</span>  Then  <span class=\"katex--inline\">a_{12}</span>  is</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } 45\\qquad \\mathrm{(B) \\ } 56\\qquad \\mathrm{(C) \\ } 67\\qquad \\mathrm{(D) \\ } 78\\qquad \\mathrm{(E) \\ } 89</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": "2002 AMC 10B Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc10B_p24", "prev": "/problem/02_amc10B_p22"}}