In the arithmetic sequence, the nth term is
[tex]a_n=a+(n-1)d[/tex]
a is the first term
d is the common difference
n is the position of the number
Since a(8) = -1
Then n = 8
Since the common difference is -8, then
d = -8
Substitute them in the rule to find the first term a
[tex]\begin{gathered} -1=a+(8-1)(-8) \\ -1=a+(7)(-8) \\ -1=a-56 \end{gathered}[/tex]
Add 56 to each side
[tex]\begin{gathered} -1+56=a-56+56 \\ 55=a \end{gathered}[/tex]
The first term is 55
The rule of the sum of the nth term is
[tex]S_n=\frac{n}{2}\lbrack a+l\rbrack[/tex]
l is the last term
Since we need the sum of 8 terms, then
a = 55
l = a(8) = -1
n = 8
[tex]\begin{gathered} S_8=\frac{8}{2}\lbrack55+(-1)\rbrack \\ S_8=4\lbrack54\rbrack \\ S_8=216 \end{gathered}[/tex]
The sum of the first 8 terms is 216
The answer is A
