Question

在数列{an}中,a1=1,a2=-3,且在数列{an}中,an+1=an+an+2,则a2012=

a(n+1)=an+a(n+2)

Answer 1

a(n+1)=an+a(n+2) (1)
a(n+2)=a(n+1)+a(n+3) (2)
(1)+(2)
a(n+1)+a(n+2)=a(n+1)+a(n+2)+an+a(n+3)
a(n+3)+an=0
a(n+3)=-an
a(n+6)=-a(n+3)=an
数列为循环数列，每6个循环一次。
2012=2+335×6
a2012=a2=-3