Question

Знайдіть  d якщо а3=4 а5=9,2
2)S10, якщо а1=14, а7=-10

Answer 1

$1)\left \{ {{a_{5} =9,2} \atop {a_{3}=4 }} \right. \\\\-\left \{ {{a_{1}+4d=9,2 } \atop {a_{1}+2d=4 }} \right.\\ ------\\2d=5,2\\\\\boxed{d=2,6}\\\\\\2)a_{1}=14 \ ; \ a_{7} =-10\\\\a_{7}=a_{1} +6d\\\\6d=a_{7}-a_{1}=-10-14=-24\\\\d=-4\\\\S_{10}=\frac{2a_{1}+9d }{2}*10=(2a_{1} +9d)*5=(2*14+9*(-4))*5=\\\\=(28-36)*5=-8*5=-40\\\\\boxed{S_{40}=-40}$