{"status": "success", "data": {"description_md": "The sequences of positive integers $1,a_2,a_3,\\ldots$ and $1,b_2,b_3,\\ldots$ are an increasing arithmetic sequence and an increasing geometric sequence, respectively. Let $c_n=a_n+b_n$. There is an integer $k$ such that $c_{k-1}=100$ and $c_{k+1}=1000$. Find $c_k$.\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 sequences of positive integers <span class=\"katex--inline\">1,a_2,a_3,\\ldots</span> and <span class=\"katex--inline\">1,b_2,b_3,\\ldots</span> are an increasing arithmetic sequence and an increasing geometric sequence, respectively. Let <span class=\"katex--inline\">c_n=a_n+b_n</span>. There is an integer <span class=\"katex--inline\">k</span> such that <span class=\"katex--inline\">c_{k-1}=100</span> and <span class=\"katex--inline\">c_{k+1}=1000</span>. Find <span class=\"katex--inline\">c_k</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": 4, "problem_name": "2016 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/16_aime_II_p10", "prev": "/problem/16_aime_II_p08"}}