设等差数列 $\left\{a_{n}\right\}$ 前 $n$ 项和为 $S_{n}$, 若 $a_{2}=3, S_{5}=35$, 则 $a_{6}=(\quad)$
解析: $\left\{\begin{array}{c}a_{2}=a_{1}+d=3 \\ S_{5}=5 a_{1}+\frac{4 \times 5}{2} d=35\end{array}\right.$ 所以 $\left\{\begin{array}{c}a_{1}+d=3 \\ a_{1}+2 d=7\end{array}\right.$ 解得 $d=4$, 所以 $a_{6}=a_{2}+4 d=19$