[tex] \Large \mathbb{SOLUTION:} [/tex]
Notice that every term of the sequence is [tex]2[/tex] less than a perfect square.
[tex] \begin{array}{ccccc} 2, &7, &14, &23, & 34, ... \\ 4 -2, &9 - 2, &16 - 2, &25 - 2, &36 - 2, ... \\ 2^2 - 2, &3^2 - 2, &4^2 - 2, &5^2- 2, &6^2 - 2, ... \end{array} [/tex]
So the general term of the sequence is
[tex] \quad \quad \begin{array}{c} a_n = (n + 1)^2 - 2 \\ \\ a_n = n^2 + 2n + 1 - 2 \\ \\ \boxed{a_n = n^2 + 2n - 1} \end{array} [/tex]
where [tex] a_n [/tex] is the nth term.
