Problem:
Define a sequence recursively by F0=0,F1=1, and Fn= the remainder when Fn−1+Fn−2 is divided by 3, for all n≥2. Thus the sequence starts 0,1,1,2,0,2,…. What is F2017+F2018+F2019+ F2020+F2021+F2022+F2023+F2024?
Answer Choices:
A. 6
B. 7
C. 8
D. 9
E. 10
Solution:
The sequence starts 0,1,1,2,0,2,2,1,0,1,1,2,… Notice that the pattern repeats and the period is 8. Thus no matter which 8 consecutive numbers are added, the answer will be 0+1+1+2+0+2+2+1=(D)9.
The problems on this page are the property of the MAA's American Mathematics Competitions