2. The third term of an arithmetic progression $a_{3}=3$, the eleventh term $a_{11}=15$.

Find the first term and the common difference of the progression.
Solution: $a_{3}=3 ; a_{11}=15$. Find $a_{1}, d$.

$\left\{\begin{array}{l}a_{1}+2 d=3, \\ a_{1}+10 d=15 ;\end{array}\left\{\begin{array}{l}8 d=12, \\ a_{1}=3-2 d ;\end{array}\left\{\begin{array}{l}d=\frac{3}{2}, \\ a_{1}=0 .\end{array}\right.\right.\right.$