11. 在等差数列 $\left\{a_{n}\right\}$ 中, 已知 $d=2, a_{n}=11, S_{n}=35$, 求 $a_{1}$ 和 $n$.
由 $\left\{\begin{array}{l}a_{n}=a_{1}+(n-1) d, \\ S_{n}=n a_{1}+\frac{n(n-1)}{2} d,\end{array}\right.$

得 $\left\{\begin{array}{l}a_{1}+2(n-1)=11, \\ n a_{1}+\frac{n(n-1)}{2} \times 2=35,\end{array}\right.$

解方程组得 $\left\{\begin{array}{l}n=5 \\ a_{1}=3\end{array}\right.$ 或 $\left\{\begin{array}{l}n=7, \\ a_{1}=-1 .\end{array}\right.$