{"status": "success", "data": {"description_md": "Define a sequence recursively by $F_{0}=0,~F_{1}=1,$ and $F_{n}=$ the remainder when $F_{n-1}+F_{n-2}$ is divided by $3,$ for all $n\\geq 2.$ Thus the sequence starts $0,1,1,2,0,2,\\ldots$ What is $F_{2017}+F_{2018}+F_{2019}+F_{2020}+F_{2021}+F_{2022}+F_{2023}+F_{2024}?$\n\n$\\textbf{(A)}\\ 6\\qquad\\textbf{(B)}\\ 7\\qquad\\textbf{(C)}\\ 8\\qquad\\textbf{(D)}\\ 9\\qquad\\textbf{(E)}\\ 10$", "description_html": "<p>Define a sequence recursively by  <span class=\"katex--inline\">F_{0}=0,~F_{1}=1,</span>  and  <span class=\"katex--inline\">F_{n}=</span>  the remainder when  <span class=\"katex--inline\">F_{n-1}+F_{n-2}</span>  is divided by  <span class=\"katex--inline\">3,</span>  for all  <span class=\"katex--inline\">n\\geq 2.</span>  Thus the sequence starts  <span class=\"katex--inline\">0,1,1,2,0,2,\\ldots</span>  What is  <span class=\"katex--inline\">F_{2017}+F_{2018}+F_{2019}+F_{2020}+F_{2021}+F_{2022}+F_{2023}+F_{2024}?</span> </p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 6\\qquad\\textbf{(B)}\\ 7\\qquad\\textbf{(C)}\\ 8\\qquad\\textbf{(D)}\\ 9\\qquad\\textbf{(E)}\\ 10</span> </p>\n<hr><p>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": "2017 AMC 10A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc10A_p14", "prev": "/problem/17_amc10A_p12"}}