{"status": "success", "data": {"description_md": "The sequence $(a_n)$ satisfies $a_0 = 0$ and $\\displaystyle a_{n + 1} = \\frac85a_n + \\frac65\\sqrt {4^n - a_n^2}$ for $n\\ge0$. Find the greatest integer less than or equal to $a_{10}$.\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>The sequence <span class=\"katex--inline\">(a_n)</span> satisfies <span class=\"katex--inline\">a_0 = 0</span> and <span class=\"katex--inline\">\\displaystyle a_{n + 1} = \\frac85a_n + \\frac65\\sqrt {4^n - a_n^2}</span> for <span class=\"katex--inline\">n\\ge0</span>. Find the greatest integer less than or equal to <span class=\"katex--inline\">a_{10}</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": 6, "problem_name": "2009 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/09_aime_II_p15", "prev": "/problem/09_aime_II_p13"}}