Question

Арифметическая прогрессия. 9 класс

Answer 1

$\left \{ {{ \frac{a_1}{a_1+d}=5} \atop { \frac{2a_1+7d}{2}\cdot 4=120}} \right.\Rightarrow \left \{ {{a_1=5a_1+5d} \atop {8a_1+28d=120}} \right.\Rightarrow \left \{ {{a_1= -\frac{5d}{4}} \atop {2a_1+7d=30}} \right.\Rightarrow\\\\ 2\cdot \frac{5d}{-4}+7d=30\\\\ -\frac{5d}{2}+7d=30\\\\ -5d+14d=60\\\\ d= \frac{60}{9}\\\\ d= \frac{20}{3}\\\\\\ a_1= -\frac{5}{4}\cdot \frac{20}{3}=- \frac{25}{3}$