(1)
n≥2时,
a(n+1)=2Sn+3
an=2S(n-1)+3
a(n+1)-an=2Sn+3-2S(n-1)-3=2an
a(n+1)=3an
a(n+1)/an=3,为定值.
又a1=3,数列{an}是以3为首项,3为公比的等比数列,通项公式为an=3ⁿ.
(2)
bn=2n-1+an=2n-1+3ⁿ
前n项和Tn=b1+b2+...+bn=2(1+2+...+n)-n+(3+3²+...+3ⁿ)
=2n(n+1)/2-n+3(3ⁿ-1)/(3-1)
=n²+3^(n+1)/2-3/2