In the circle $x^{2}+y^{2}-5 x=0$, there are exactly $n$ chords passing through the point $\left(\frac{5}{2}, \frac{3}{2}\right)$ whose lengths form an arithmetic sequence, with the common difference $d \in$ $\left(-\frac{1}{6}, \frac{1}{3}\right]$, then the set of values for $n$ is
(A) $|4,5,6|$
(B) $66,7,8,9 \vdots$
(C) $\{3,4,5\}$
(D) $\{3,4,5,6\}$
2. (A).

Given, the shortest chord length of a circle passing through the point $\left(\frac{5}{2}, \frac{3}{2}\right)$ is 1, and the longest is 5, from this we can draw the conclusion.