Question 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 $$
F_{2017}+F_{2018}+F_{2019}+F_{2020}+
$$$$
F_{2021}+F_{2022}+F_{2023}+F_{2024}?
$$
F_{2017}+F_{2018}+F_{2019}+F_{2020}+
$$$$
F_{2021}+F_{2022}+F_{2023}+F_{2024}?
$$