{"status": "success", "data": {"description_md": "The sequence $a_0,a_1,a_2,\\cdots$ is a strictly increasing arithmetic sequence of positive integers such that $$2^{a_7}=2^{27} \\cdot a_7.$$ What is the minimum possible value of $a_2$?\n\n$\\textbf{(A) }\\ 8 \\qquad \\textbf{(B) }\\ 12 \\qquad \\textbf{(C) }\\ 16 \\qquad \\textbf{(D) }\\ 17 \\qquad \\textbf{(E) }\\ 22$\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  <span class=\"katex--inline\">a_0,a_1,a_2,\\cdots</span>  is a strictly increasing arithmetic sequence of positive integers such that  <span class=\"katex--display\">2^{a_7}=2^{27} \\cdot a_7.</span>  What is the minimum possible value of  <span class=\"katex--inline\">a_2</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }\\ 8 \\qquad \\textbf{(B) }\\ 12 \\qquad \\textbf{(C) }\\ 16 \\qquad \\textbf{(D) }\\ 17 \\qquad \\textbf{(E) }\\ 22</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": 2, "problem_name": "2022 AMC 12B Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12B_p10", "prev": "/problem/22_amc12B_p08"}}