Viết lại ta được: $U_n+2.2^n-n-\frac{3}{2}=3(U_{n-1}+2.2^{n-1}-(n-1)-\frac{3}{2})$Đặt $V_n=U_n+2.2^n-n-\frac{3}{2}$
Ta có: $V_n=3.V_{n-1}=3^{n-1}.V_1=3^{n-1}(U_1+\frac{3}{2})=\frac{11.3^{n-1}}{2}$
$\Rightarrow U_n=\frac{11}{2}.3^{n-1}-2.2^n+n+\frac{3}{2}$