a(n+1)=2an+3a(n+1)+k=2an+3+k=2(an+3/2+k/2)则令k=3/2+k/2k=3则两边同时加3a(n+1)+3=2(an+3)[a(n+1)+3]/(an+3)=2所以an+3是等比数列,q=2a1+3=4所以an+3=4*2^(n-1)an=4*2^(n-1)-3 =2^(n+1)-3