{"status": "success", "data": {"description_md": "A sequence $a_1, a_2, a_3, \\ldots$ is defined as follows: $a_1=1$, $a_2=3$, and $a_n = 2a_{n-1} - a_{n-2} + 2$ for $n \\geq 3$. Find $a_{25}$.", "description_html": "<p>A sequence <span class=\"katex--inline\">a_1, a_2, a_3, \\ldots</span> is defined as follows: <span class=\"katex--inline\">a_1=1</span>, <span class=\"katex--inline\">a_2=3</span>, and <span class=\"katex--inline\">a_n = 2a_{n-1} - a_{n-2} + 2</span> for <span class=\"katex--inline\">n \\geq 3</span>. Find <span class=\"katex--inline\">a_{25}</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "TxO Math Bowl 2024 - Individuals A - Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024indivsA-p10", "prev": "/problem/txo2024indivsA-p08"}}