Explanation:
The arithmetic series is given below as
[tex]\sum_{k\mathop{=}0}^{18}2k+7[/tex]
Step 1:
Figure out the first term and the second term
[tex]\begin{gathered} k=1 \\ 2k+7=2(1)+7=9 \\ k=2 \\ 2k+7=2(2)+7=11 \end{gathered}[/tex]
Step 2:
Calculate the common difference
[tex]\begin{gathered} d=t_2-t_1 \\ d=11-9 \\ d=2 \end{gathered}[/tex]
Step 3:
Calculate the sum of the arithmetic series using the formula below
[tex]\begin{gathered} S_n=\frac{n}{2}(2a+(n-1)d) \\ where, \\ n=18 \\ a=9 \\ d=2 \end{gathered}[/tex]
By substituting the values, we will have
[tex][/tex]
