{"status": "success", "data": {"description_md": "The sequence\n\n$\\log_{12}{162}$, $\\log_{12}{x}$, $\\log_{12}{y}$, $\\log_{12}{z}$, $\\log_{12}{1250}$<br>is an arithmetic progression. What is $x$?\n\n$\\textbf{(A)} \\ 125\\sqrt{3} \\qquad \\textbf{(B)} \\ 270 \\qquad \\textbf{(C)} \\ 162\\sqrt{5} \\qquad \\textbf{(D)} \\ 434 \\qquad \\textbf{(E)} \\ 225\\sqrt{6}$\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>The sequence</p>&#10;<p> <span class=\"katex--inline\">\\log_{12}{162}</span> ,  <span class=\"katex--inline\">\\log_{12}{x}</span> ,  <span class=\"katex--inline\">\\log_{12}{y}</span> ,  <span class=\"katex--inline\">\\log_{12}{z}</span> ,  <span class=\"katex--inline\">\\log_{12}{1250}</span> <br/>is an arithmetic progression. What is  <span class=\"katex--inline\">x</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} \\ 125\\sqrt{3} \\qquad \\textbf{(B)} \\ 270 \\qquad \\textbf{(C)} \\ 162\\sqrt{5} \\qquad \\textbf{(D)} \\ 434 \\qquad \\textbf{(E)} \\ 225\\sqrt{6}</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": "2013 AMC 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12A_p15", "prev": "/problem/13_amc12A_p13"}}