[tex]a_n=n^2+3n\\\\a_1=1^2+3\cdot1=4\\a_{n+1}=(n+1)^2+3(n+1)=n^2+2n+1+3n+3=n^2+3n+2n+1=\\=a_n+2n+1\\\\\Large \boxed{\left\{\begin{array}{ll}a_1=4\\a_{n+1}=a_n+2n+1\end{array}\right.}[/tex]
