{"status": "success", "data": {"description_md": "Define a sequence recursively by $t_1 = 20$, $t_2 = 21$, and $$t_n = \\frac{5t_{n-1}+1}{25t_{n-2}} $$for all $n \\ge 3$. Then $t_{2020}$ can be written as $\\frac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.\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": "

Define a sequence recursively by t_1 = 20, t_2 = 21, andt_n = \\frac{5t_{n-1}+1}{25t_{n-2}}for all n \\ge 3. Then t_{2020} can be written as \\frac{p}{q}, where p and q are relatively prime positive integers. Find p+q.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2020 AIME II Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/20_aime_II_p07", "prev": "/problem/20_aime_II_p05"}}