Answer:
The sum of the first twenty-seven terms is 1,188
Step-by-step explanation:
we know that
The formula of the sum in arithmetic sequence is equal to
[tex]S=\frac{n}{2}[2a1+(n-1)d][/tex]
where
n is the number of terms
a1 is the first term
d is the common difference (constant)
step 1
Find the common difference d
we have
n=7
a1=-8
S=28
substitute and solve for d
[tex]28=\frac{7}{2}[2(-8)+(7-1)d][/tex]
[tex]28=\frac{7}{2}[-16+(6)d][/tex]
[tex]8=[-16+(6)d][/tex]
[tex]8+16=(6)d[/tex]
[tex]d=24/(6)=4[/tex]
step 2
Find the sum of the first twenty-seven terms
we have
n=27
a1=-8
d=4
substitute
[tex]S=\frac{27}{2}[2(-8)+(27-1)(4)][/tex]
[tex]S=\frac{27}{2}[(-16)+(104)][/tex]
[tex]S=\frac{27}{2}88][/tex]
[tex]S=1,188[/tex]
