4. Let $A$ and $B$ be the two foci of a hyperbola, and point $C$ lies on the hyperbola. It is known that the three sides of $\triangle A B C$ form an arithmetic sequence, and $\angle A C B=120^{\circ}$. Then the eccentricity of the hyperbola is $\qquad$
4. $\frac{7}{2}$.

According to the problem, we can assume $|A C|+|A B|=2|B C|$, and
$$
\begin{array}{l}
|A C|^{2}+|B C|^{2}-|A B|^{2} \\
=2|A C||B C| \cos 120^{\circ} .
\end{array}
$$

From this, $|A C|:|A B|:|B C|=3: 7: 5$.
Thus, the eccentricity of the hyperbola is $\frac{7}{2}$.