Question

Sa se determine primul termen si ratia progresiei aritmetice (an) daca: a3=-4, S15=-285.

Answer 1

$\displaystyle a_3=-4,~S_{15}=-285,~a_1=?,~r=? \\ a_3=-4 \Rightarrow a_{3-1}+r=-4 \Rightarrow a_2+r=-4 \Rightarrow a_1+2r=-4 \Rightarrow \\ \Rightarrow a_1=-4-2r \\ S_{15}=-285 \\ \frac{2 (-4-2r)+(15-1) \cdot r}{2} \cdot 15=-285 \\ \frac{-8-4r+14r}{2}\cdot 15=-285 \\ \frac{-8+10r}{2} \cdot 15=-285 \\ -120+150r=-285 \cdot 2 \\ -120+150r=-570 \\ 150r=-570+120 \\ 150r=-450 \\ r=-3 \\ a_1=-4-2r \Rightarrow a_1=-4-2 \cdot (-3) \Rightarrow a_1=-4+6 \Rightarrow a_1=2$