{"status": "success", "data": {"description_md": "Define the sequence $a_1,a_2,a_3,\\ldots$ by $a_n=\\sum_{k=1}^n\\sin(k)$, where $k$ represents radian measure. Find the index of the $100$th term for which $a_n<0$.\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>Define the sequence <span class=\"katex--inline\">a_1,a_2,a_3,\\ldots</span> by <span class=\"katex--inline\">a_n=\\sum_{k=1}^n\\sin(k)</span>, where <span class=\"katex--inline\">k</span> represents radian measure. Find the index of the <span class=\"katex--inline\">100</span>th term for which <span class=\"katex--inline\">a_n&lt;0</span>.</p>&#10;<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2015 AIME II Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/15_aime_II_p14", "prev": "/problem/15_aime_II_p12"}}