a(n+2)=-4a(n+1)+5an
===> a(n+2)-a(n+1)=-5[a(n+1)-an]
===> [a(n+2)-a(n+1)]/[a(n+1)-an]=-5
===> 数列{a(n+1)-an}是公比为-5的等比数列.
a2-a1=2 ===> a(n+1)-an=2(-5)^(n-1).
a2-a1=2
a3-a2=2(-5)
……
an-a(n-1)=2(-5)^(n-2)
相加：an-a1=2[1-(-5)^(n-1)]/(1+5)=[1-(-5)^(n-1)]/3
===> an=[4-(-5)^(n-1)]/3.