{"status": "success", "data": {"description_md": "A sequence of integers $a_1$, $a_2$, $a_3$, $\\ldots$ is chosen so that $a_n = a_{n - 1} - a_{n - 2}$ for each $n \\ge 3$. What is the sum of the first 2001 terms of this sequence if the sum of the first 1492 terms is 1985, and the sum of the first 1985 terms is 1492?\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>A sequence of integers <span class=\"katex--inline\">a_1</span>, <span class=\"katex--inline\">a_2</span>, <span class=\"katex--inline\">a_3</span>, <span class=\"katex--inline\">\\ldots</span> is chosen so that <span class=\"katex--inline\">a_n = a_{n - 1} - a_{n - 2}</span> for each <span class=\"katex--inline\">n \\ge 3</span>. What is the sum of the first 2001 terms of this sequence if the sum of the first 1492 terms is 1985, and the sum of the first 1985 terms is 1492?</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": 3, "problem_name": "1985 AIME Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/85_aime_p06", "prev": "/problem/85_aime_p04"}}