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# Using mathematical induction, the numbers $a_n\;'s$ are defined by, $a_0=1,a_{n+1}=3n^2+n+a_n( n \geq 0)$. Then $a_n=$

$\begin {array} {1 1} (1)\;n^3+n^2+1 & \quad (2)\;n^3-n^2+1 \\ (3)\;n^3-n^2 & \quad (4)\;n^3+n^2 \end {array}$

$(2)\;n^3-n^2+1$