Question

s7 = 105, a7 = -6, s15 = 121,5. а15 = 11,6. (а) Найдите первый член и разность арифметической прогрессии​

Answer 1

$1)S_{7} =105\\\\ a_{7}=-6\\\\S_{7}=\frac{a_{1}+a_{7}}{2}*7\\\\105=\frac{a_{1} -6}{2}*7\\\\210=(a_{1}-6)*7\\\\a_{1}-6=30\\\\a_{1}=36\\\\a_{7}=a_{1} +6d\\\\-6=36+6d\\\\6d=-42\\\\d=-7\\\\Otvet:\boxed{a_{1}=36;d=-7}$

$2)S_{15} =121,5\\\\ a_{15}=11,6\\\\S_{15}=\frac{a_{1}+a_{15}}{2}*15\\\\121,5=\frac{a_{1} +11,6}{2}*15\\\\243=(a_{1}+11,6)*15\\\\a_{1}+11,6=16,2\\\\a_{1}=4,6\\\\a_{15}=a_{1} +14d\\\\11,6=4,6+14d\\\\14d=7\\\\d=0,5\\\\Otvet:\boxed{a_{1}=4,6;d=0,5}$