Respuesta :
Hello!
With this informations, we have to find the ratio of this sequence, using the formula below:
[tex]\begin{gathered} a_n=a_1+(n-1)\cdot r \\ 33=12+(8-1)\cdot r \\ 33=12+7r \\ 33-12=7r \\ 21=7r \\ r=\frac{21}{7} \\ \boxed{r=3} \end{gathered}[/tex]So, this arithmetic series will be:
[tex]\begin{gathered} a_1=12 \\ a_2=15 \\ a_3=18 \\ a_4=21 \\ a_5=24 \\ a_6=27 \\ a_7=30 \\ a_8=33 \end{gathered}[/tex]To finish, let's calculate the sum of the terms of this sequence using the formula:
[tex]\begin{gathered} S_n=\frac{(a_1+a_n)\cdot n}{2}=\frac{(12+33)\cdot8}{2}=\frac{45\cdot8}{2}=\frac{360}{2}=180 \\ \\ \boxed{S_n=180} \end{gathered}[/tex]