Question

12. Знайдіть перший член і різницю арифметичної прогресії (а, ), якщо a 2 + a 15 = 74 i a + a = 94 17 ​

Answer 1

$\displaystyle\bf\\\left \{ {{a_{2} +a_{15} =74} \atop {a_{5} +a_{17} =94}} \right. \\\\\\\left \{ {{a_{1} +d+a_{1}+14d =74} \atop {a_{1} +4d+a_{1}+16d =94}} \right. \\\\\\\left \{ {{2a_{1} +15d =74} \ |\cdot(-1) \atop {2a_{1} +20d =94}} \right. \\\\\\+\left \{ {{-2a_{1} -15d =-74} \atop {2a_{1} +20d =94}} \right. \\------------\\5d=20\\\\d=4\\\\2a_{1} =74-15d=74-15\cdot 4=74-60=14\\\\a_{1} =7\\\\\\Otvet \ : \ a_{1} =7 \ \ ; \ \ d=4$