-558
Explanation
The arithmetic sequence formula is given as
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \text{where} \\ a_1\text{ is the first term} \\ d\text{ is the common difference} \end{gathered}[/tex]Step 1
a)
Let
[tex]\begin{gathered} a_1=-8 \\ a_2=-15 \\ a_3=-22 \\ a_4=-29 \end{gathered}[/tex]b) find the common difference
[tex]\begin{gathered} a_2-a_1=-15-(-8)=-15+8=-7 \\ a_3-a_2=-22-(-15)=-22+15=-7 \\ a_4-a_3=-29-(-22)=-29+22+8=-7 \end{gathered}[/tex]so, the common diference is -7
c) now replace in the original formula
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ a_n=-8_{}+(n-1)(-7) \end{gathered}[/tex]therefore, the serie is
[tex]a_n=-8_{}+(n-1)(-7)[/tex]Step 2
now, to find the sum, we need to apply the formula
[tex]S=\frac{n(a_1+a_n)}{2}[/tex]so
a) find an
n=12
[tex]\begin{gathered} a_n=-8_{}+(n-1)(-7) \\ a_{12}=-8_{}+(12-1)(-7)=-8-77=-85 \end{gathered}[/tex]now, replace in the formula
[tex]\begin{gathered} S=\frac{12(-8_{}-85)}{2} \\ S=\frac{12(-93)}{2} \\ S=\frac{-1116}{2} \\ s=-558 \end{gathered}[/tex]therefore, the answer is
-558
I hope this helps you
