Question

Найдите сумму первыз двадцати членов арифметической прогрессии cn если c7=18,5 и c17=- 26, 5

Answer 1

$c_{7}=18,5\\\\c_{17}=-26,5\\\\S_{20}=?\\\\\left \{ {{c_{17}=.26,5 } \atop {c_{7}=18,5 }} \right.\\\\-\left \{ {{c_{1}+16d=-26,5 } \atop {c_{1}+6d=18,5 }} \right.\\--------\\10d=-45\\\\d=-4,5\\\\c_{1}=18,5-6d=18,5-6*(-4,5)=18,5+27=45,5\\\\c_{20}=c_{1}+19d=45,5+19*(-4,5)=45,5-85,5=-40\\\\S_{20}=\frac{c_{1}+c_{20}}{2} *20=(c_{1}+c_{20})*10=(45,5-40)*10=5,5*10=55$