Proof Writing & Problem Solving · Medium problem

Define $a_1 = 1$ and $a_n = a_{n-1} + 3n - 2$ for $n \ge 2$. Compute the first few terms, guess a formula of the form $a_n = \dfrac{n(pn - q)}{2}$, and prove it by induction. What is $a_{10}$?