a1=1,a2=5,a(N+1)+2an=3a(n-1),设数列cn满足Cn=a(n+1)-an,求证Cn是等比,求Cn

a(N+1)-an+3an=3a(n-1)
a(N+1)-an=3a(n-1)-3an
a(N+1)-an=-3(an-a(n-1))
Cn=-3C（n-1)
所以Cn是等比,且公比为-3
C1=A2-A1=5-1=4
所以Cn=4*(-3)^(n-1)