Question

对于数列{a_n},a₁=4,a_n+1=f(a_n),依照下表则a₂₀₁₅等于(　　)

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

 (A)2   (B)3    (C)4    (D)5

Answer 1

D解析:由题意a₂=f(a₁)=f(4)=1,a₃=f(a₂)=f(1)=5,

a₄=f(a₃)=f(5)=2,a₅=f(a₄)=f(2)=4,a₆=f(a₅)=f(4)=1.

则数列{a_n}的项周期性出现,其周期为4,a₂₀₁₅=a_4×503+3=a₃=5.故选D.