Question

Найдите a1, если d=-20; S4=300​

Answer 1

$S_{n}=\frac{a_{1}+a_{n}}{2}\cdot n$

$a_{n}=a_{1}+d\cdot (n-1)$

$S_{4}=\frac{a_{1}+a_{4}}{2}\cdot 4=\frac{a_{1}+a_{1}+3d}{2}\cdot 4=(2a_{1}+3d)\cdot 2$

$S_{4}=300\\\\(2a_{1}+3d)\cdot 2=300$

$d=-20$

$(2a_{1}+3\cdot (-20))\cdot 2=300$

$(2a_{1}-60)\cdot 2=300$

$2a_{1}-60=150$

$2a_{1}=150+60$

$2a_{1}=210$

$a_{1}=105$