Answer:
A
Step-by-step explanation:
Given sequence [tex]-8,\ -1,\ 6,\ ...[/tex]
In this sequence,
[tex]a_1=-8\\ \\a_2=-1\\ \\a_3=6\\ \\...[/tex]
Hence,
[tex]d=a_2-a_1=-1-(-8)=7\\ \\d=a_3-a_2=6-(-1)=7[/tex]
Find 56th term:
[tex]a_{n}=a_1+(n-1)\cdot d\\ \\a_{56}=-8+(56-1)\cdot 7\\ \\a_{56}=-8+385\\ \\a_{56}=377[/tex]
The sum of 56 terms is
[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\ \\S_{56}=\dfrac{-8+377}{2}\cdot 56=\dfrac{369}{2}\cdot 56=369\cdot 28=10,332[/tex]
