{"status": "success", "data": {"description_md": "A geometric sequence $(a_n)$ has $a_1=\\sin x$, $a_2=\\cos x$, and $a_3= \\tan x$ for some real number $x$. For what value of $n$ does $a_n=1+\\cos x$?\n\n$\\textbf{(A)}\\ 4 \\qquad \\textbf{(B)}\\ 5 \\qquad \\textbf{(C)}\\ 6 \\qquad \\textbf{(D)}\\ 7 \\qquad \\textbf{(E)}\\ 8$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A geometric sequence  <span class=\"katex--inline\">(a_n)</span>  has  <span class=\"katex--inline\">a_1=\\sin x</span> ,  <span class=\"katex--inline\">a_2=\\cos x</span> , and  <span class=\"katex--inline\">a_3= \\tan x</span>  for some real number  <span class=\"katex--inline\">x</span> . For what value of  <span class=\"katex--inline\">n</span>  does  <span class=\"katex--inline\">a_n=1+\\cos x</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 4 \\qquad \\textbf{(B)}\\ 5 \\qquad \\textbf{(C)}\\ 6 \\qquad \\textbf{(D)}\\ 7 \\qquad \\textbf{(E)}\\ 8</span> </p>&#10;<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": "2010 AMC 12B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12B_p21", "prev": "/problem/10_amc12B_p19"}}