2017 AMC 10A Problem 13

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}?

\textbf{(A)}\ 6\qquad\textbf{(B)}\ 7\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 10

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.