Question

Evaluate each arithmetic series described A1=12, an=33, n=8

Answer 1

Hello!

With this informations, we have to find the ratio of this sequence, using the formula below:

`\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=(21)/(7) \\ \boxed{r=3} \end{gathered}`

So, this arithmetic series will be:

`\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}`

To finish, let's calculate the sum of the terms of this sequence using the formula:

`\begin{gathered} S_n=((a_1+a_n)\cdot n)/(2)=((12+33)\cdot8)/(2)=(45\cdot8)/(2)=(360)/(2)=180 \\ \\ \boxed{S_n=180} \end{gathered}`