{"status": "success", "data": {"description_md": "For any sequence of real numbers $A=(a_1,a_2,a_3,\\ldots)$, define $\\Delta A$ to be the sequence $(a_2-a_1,a_3-a_2,a_4-a_3,\\ldots)$, whose $n^\\text{th}$ term is $a_{n+1}-a_n$. Suppose that all of the terms of the sequence $\\Delta(\\Delta A)$ are $1$, and that $a_{19}=a_{92}=0$. Find $a_1$.\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": "

For any sequence of real numbers A=(a_1,a_2,a_3,\\ldots), define \\Delta A to be the sequence (a_2-a_1,a_3-a_2,a_4-a_3,\\ldots), whose n^\\text{th} term is a_{n+1}-a_n. Suppose that all of the terms of the sequence \\Delta(\\Delta A) are 1, and that a_{19}=a_{92}=0. Find a_1.

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": "1992 AIME Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/92_aime_p09", "prev": "/problem/92_aime_p07"}}