{"status": "success", "data": {"description_md": "Two geometric sequences $a_1,a_2,a_3,\\ldots$ and $b_1,b_2,b_3\\ldots$ have the same common ratio, with $a_1=27$,$b_1=99$, and $a_{15}=b_{11}$. Find $a_9.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>Two geometric sequences <span class=\"katex--inline\">a_1,a_2,a_3,\\ldots</span> and <span class=\"katex--inline\">b_1,b_2,b_3\\ldots</span> have the same common ratio, with <span class=\"katex--inline\">a_1=27</span>,<span class=\"katex--inline\">b_1=99</span>, and <span class=\"katex--inline\">a_{15}=b_{11}</span>. Find <span class=\"katex--inline\">a_9.</span></p>&#10;<hr/>&#10;<p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2012 AIME II Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/12_aime_II_p03", "prev": "/problem/12_aime_II_p01"}}