数列{an}中,an=-(2n+3)/2,前n项和为An,数列{bn}前n项和为Bn,且有4Bn-12An=13n,试求

数列{an}的通项公式是an=-(2n+3)/2,说明{an}是等差数列
a1=-(2+3)/2=-5/2
所以An=n(a1+an)/2=n*(-5/2-(2n+3)/2)/2=-n(n+4)/2
又4Bn-12An=13n
所以Bn=(12An+13n)/4=(-6n(n+4)+13n)/4=-(6n^2+11n)/4
所以b1=B1=-17/4
当n≥时,bn=Bn-B(n-1)=-(6n^2+11n)/4+(6(n-1)^2+11(n-1))/4=-(12n+5)/4
经检验发现b1=-17/4也满足bn=-(12n+5)/4
所以bn=-(12n+5)/4