(14) Let the sequence $\left\{a_{n}\right\}$ have all positive terms, and $S_{n}$ be the sum of its first $n$ terms. For any positive integer $n$, the arithmetic mean of $a_{n}$ and 2 equals the geometric mean of $S_{n}$ and 2, then the general term formula of the sequence is $\qquad$ .
(14) $a_{n}=4 n-2$