2017 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 13 Medium

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≥ 2. Thus the sequence starts 0, 1, 1, 2, 0, 2, \cdots. What is F_{2017}+F_{2018}+F_{2019}+F_{2020}+F_{2021}+F_{2022}+F_{2023}+F_{2024}? (2017 AMC 10A Problem, Question#13)

  • A.

    6

  • B.

    7

  • C.

    8

  • D.

    9

  • E.

    10

Answer:D

A patten starts to emerge as the function is continued. The repeating patten is 0, 1, 1, 2, 0, 2, 2, 1 \ldots. The problem asks for the sum of eight consecutive terms in the sequence.

Because there are eight numbers in the repeating sequence, we just need to find the sum of the numbers in the sequence, which is (\rm D) 9.

Related Problems
Problem 11 2017 AMC 10 A
Problem 12 2017 AMC 10 A
Problem 14 2017 AMC 10 A
Problem 15 2017 AMC 10 A
Think Academy Powered by ChatGPT