1. Let $\left\{a_{n}\right\}$ be an arithmetic sequence with the sum of the first $n$ terms denoted as $S_{n}$. If $S_{2}=10, S_{5}=55$, then a direction vector of the line passing through points $P\left(n, a_{n}\right)$ and $Q(n+2$, $a_{n+2})$ can be ( ).
(A) $\left(2, \frac{1}{2}\right)$
(B) $\left(-\frac{1}{2},-2\right)$
(C) $\left(-\frac{1}{2},-1\right)$
(D) $(-1,-1)$
-1.B.
Let $\left\{a_{n}\right\}$ be an arithmetic sequence with a common difference of $d$. Then $\left\{\begin{array}{l}S_{2}=2 a_{1}+d=10, \\ S_{5}=5 a_{1}+10 d=55\end{array} \Rightarrow\left\{\begin{array}{l}a_{1}=3, \\ d=4 .\end{array}\right.\right.$

Therefore, $k_{P Q}=\frac{a_{n+2}-a_{n}}{(n+2)-n}=d=4$.