9. In an arithmetic sequence $\left\{a_{n}\right\}$ with a common difference not equal to 0, $a_{4}=10$, and $a_{3} 、 a_{6} 、 a_{10}$ form a geometric sequence. Then the general term formula of the sequence $\left\{a_{n}\right\}$ is $\qquad$
9. $n+6$.

Let $\left\{a_{n}\right\}$ be an arithmetic sequence with a common difference of $d(d \neq 0)$.
From the given information, we have
$$
(10+2 d)^{2}=(10-d)(10+6 d) \Rightarrow d=1 \text {. }
$$

Thus, $a_{n}=a_{4}+(n-4) d=n+6$.