a(n+1)=2an+3
a(n+1)+k=2an+3+k=2(an+3/2+k/2)
则令k=3/2+k/2
k=3
则两边同时加3
a(n+1)+3=2(an+3)
[a(n+1)+3]/(an+3)=2
所以an+3是等比数列,q=2
a1+3=5
所以an+3=5*2^(n-1)
an=5*2^(n-1)-3