3. For the arithmetic sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$, the sums of the first $n$ terms are $S_{n}$ and $T_{n}$, respectively. For all positive integers $n$, $\frac{S_{n}}{T_{n}}=\frac{2 n}{3 n+1}$. Then $\frac{a_{7}}{b_{9}}$ equals ( ).
(A) $\frac{7}{9}$
(B) $\frac{14}{27}$
(C) $\frac{2}{9}$
(D) $\frac{1}{2}$
3. D.

Using the property of the sum of the first $n$ terms of an arithmetic sequence, we can set
$$
S_{n}=2 k n^{2}, T_{n}=k(3 n+1) n .
$$