Question

Знайдіть різницю та перший член арифметичної прогресії, якщо a3 + a7 = 30 i a6 + a16 = 60.​

Answer 1

$\displaystyle\bf\\\left \{ {{a_{6} +a_{16} =60} \atop {a_{3} +a_{7} =30}} \right. \\\\\\\left \{ {{a_{1} +5d+a_{1} +15d=60} \atop {a_{1} +2d+a_{1} +6d=30}} \right.\\\\\\-\left \{ {{2a_{1} +20d=60} \atop {2a_{1} +8d =30}} \right. \\----------\\12d=30\\\\d=30:12\\\\\boxed{d=2,5}\\\\\\2a_{1} +8d=30 \ |:2\\\\a_{1} +4d=15\\\\a_{1} =15-4d=15-4\cdot 2,5=15-10=5\\\\\boxed{a_{1} =5}$