Question

设f(x)定义如表，数列{x_n}满足x₁＝5，x_n＋1＝f(x_n)，则x₂₀₁₄的值为________.

x	1	2	3	4	5	6
f(x)	4	5	1	2	6	3

Answer 1

　1

[解析]　由条件知x₁＝5，x₂＝f(x₁)＝f(5)＝6，x₃＝f(x₂)＝f(6)＝3，x₄＝f(x₃)＝f(3)＝1，x₅＝f(x₄)＝f(1)＝4，x₆＝f(x₅)＝f(4)＝2，x₇＝f(x₆)＝f(2)＝5＝x₁，可知{x_n}是周期为6的周期数列，∴x₂₀₁₄＝x₄＝1.