a(n+2)+2an=3a(n+1)
a(n+2)-a(n+1)=2a(n+1)-2an
[a(n+2)-a(n+1)]/[a(n+1)-2an]=2
∴數(shù)列{an+1-an}是等比數(shù)列
a(n+1)-an=(a2-a1)q^(n-1)
=(4-(-1))2^(n-1)
=5*2^(n-1)
an-a(n-1)=5*2^(n-2)
.
a2-a1=(4-(-1))=5=5*2^0
相加得
a(n+1)-a1=5(2^0+2^1+.2^(n-1))
=5*(1*(2^n-1)/(2-1))
=5*2^n-5
a(n+1)=5*2^n-5+a1=5*2^n-6
an=5*2^(n-1)-6