{"status": "success", "data": {"description_md": "A function $f$ is defined recursively by $f(1)=f(2)=1$ and $$f(n)=f(n-1)-f(n-2)+n$$for all integers $n \\geq 3$. What is $f(2018)$?\n\n$\\textbf{(A) } 2016 \\qquad \\textbf{(B) } 2017 \\qquad \\textbf{(C) } 2018 \\qquad \\textbf{(D) } 2019 \\qquad \\textbf{(E) } 2020$", "description_html": "<p>A function  <span class=\"katex--inline\">f</span>  is defined recursively by  <span class=\"katex--inline\">f(1)=f(2)=1</span>  and  <span class=\"katex--display\">f(n)=f(n-1)-f(n-2)+n</span> for all integers  <span class=\"katex--inline\">n \\geq 3</span> . What is  <span class=\"katex--inline\">f(2018)</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 2016 \\qquad \\textbf{(B) } 2017 \\qquad \\textbf{(C) } 2018 \\qquad \\textbf{(D) } 2019 \\qquad \\textbf{(E) } 2020</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": "2018 AMC 10B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10B_p21", "prev": "/problem/18_amc10B_p19"}}