Verified answer

Ответ:

[tex]20[/tex]

Объяснение:

[tex]a_1=-5\\\\d=6\\\\S_n=1040[/tex]

[tex]S_n=[a_1+\frac{(n-1)d}{2}]\cdot n[/tex]

[tex][-5+\frac{(n-1)\cdot 6}{2}]\cdot n=1040[/tex]

[tex]\\\\\left [-5+3(n-1) \right ] \cdot n=1040\\\\ -5n+3n(n-1)=1040\\\\-5n+3n^2-3n-1040=0\\\\3n^2-8n-1040=0\\\\D=(-8)^2-4\cdot 3\cdot (-1040)=64+12480=12544\\\\\sqrt{D}=\sqrt{12544}=112\\\\n_1=\frac{8-112}{2\cdot 3}=\frac{-104}{6}=-\frac{53}{3}\not \in N\\\\n_2=\frac{8+112}{2\cdot 3}=\frac{120}{6}=20[/tex]