4. Given a geometric sequence $\left\{a_{n}\right\}$ with common ratio $q \neq 1$, and $a_{m} 、 a_{n} 、 a_{p}$ also form a geometric sequence, $m$ 、 $n, p(\quad)$.
A. form an arithmetic sequence
B. form a geometric sequence
C. form both an arithmetic sequence and a geometric sequence
D. form neither an arithmetic sequence nor a geometric sequence
4. A.

From the formulas $a_{m}=a_{1} q^{m-1}, a_{n}=a_{1} q^{n-1}, a_{p}=a_{1} q^{p-1}$, then $a_{m} \cdot a_{p}=a_{n}^{2}$, so $q^{m+p-2}=q^{2 n-2}$. Therefore, $m+p=2 n$.