2. Find the sum of the first fifteen terms of an arithmetic progression if its third term is -5, and the fifth term is 2.4.
Solution: $a_{3}=-5 ; a_{5}=2.4, S_{15}=$ ?

$\left\{\begin{array}{l}a_{1}+2 d=-5, \\ a_{1}+4 d=2.4 ;\end{array} 2 d=7.4, d=3.7 ; d_{1}=-5-2 d=-12.4\right.$,

$S_{15}=\frac{2 \cdot(-12.4)+3.7 \cdot 14}{2} \cdot 15=202.5$. Answer: $S_{15}=202.5$