2. Find the sum of the first twelve terms of an arithmetic progression if its fifth term $a_{5}=1$, and the seventeenth term $a_{17}=18$.
Solution: $a_{5}=1 ; a_{17}=18$. Find $S_{12}$.

$$
\left\{\begin{array} { l } 
{ a _ { 1 } + 4 d = 1 , } \\
{ a _ { 1 } + 1 6 d = 1 8 ; }
\end{array} \left\{\begin{array}{l}
12 d=17, \\
a_{1}=1-4 \frac{17}{12}=-\frac{14}{3} ;
\end{array} \quad S_{12}=\frac{2 \cdot\left(-\frac{14}{3}\right)+\frac{17}{12} \cdot 11}{2} \cdot 12=37.5\right.\right.
$$

Answer: 37.5 .