Question

Sa se determine primul termen al unei progresii aritmetice (an)n≥1,stiind ca r=-2 si a₃+a₇=12.

Answer 1

$\displaystyle r=-2,~a_3+a_7=12 \\ a_3+a_7=12 \\ a_{3-1}+r+a_{7-1}+r=12 \\ a_2+r+a_6+r=12 \\ a_1+2r+a_1+6r=12 \\ 2a_1+8r=12 \\ 2a_1+8 \cdot (-2)=12 \\ 2a_1-16=12 \\ 2a_1=12+16 \\ 2a_1=28 \\ a_1=28:2 \\ \boxed{a_1=14}$