{"status": "success", "data": {"description_md": "Suppose that $(u_n)$ is a [[sequence]] of real numbers satisfying $u_{n+2}=2u_{n+1}+u_n$,\nand that $u_3=9$ and $u_6=128$. What is $u_5$?\n\n$\\mathrm{(A)}\\ 40\\qquad\\mathrm{(B)}\\ 53\\qquad\\mathrm{(C)}\\ 68\\qquad\\mathrm{(D)}\\ 88\\qquad\\mathrm{(E)}\\ 104$", "description_html": "<p>Suppose that  <span class=\"katex--inline\">(u_n)</span>  is a [[sequence]] of real numbers satisfying  <span class=\"katex--inline\">u_{n+2}=2u_{n+1}+u_n</span> ,<br/>\nand that  <span class=\"katex--inline\">u_3=9</span>  and  <span class=\"katex--inline\">u_6=128</span> . What is  <span class=\"katex--inline\">u_5</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 40\\qquad\\mathrm{(B)}\\ 53\\qquad\\mathrm{(C)}\\ 68\\qquad\\mathrm{(D)}\\ 88\\qquad\\mathrm{(E)}\\ 104</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": "2008 AMC 10B Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc10B_p12", "prev": "/problem/08_amc10B_p10"}}