To find the sum of the first n terms of an arithmetic sequence, we use the formula (which you also gave):
[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]
Let's find a1 first by substituting 1 for i.
[tex]\begin{gathered} a_i=-5i \\ a_1=-5(1) \\ a_1=-5 \end{gathered}[/tex]
Next, let's solve for the last term, a30.
[tex]\begin{gathered} a_{30}=-5(30) \\ a_{30}=-150 \end{gathered}[/tex]
Let's use these values to solve for the sum.
[tex]\begin{gathered} S_{30}=\frac{30[-5+(-150)]}{2} \\ \\ S_{30}=\frac{30(-155)}{2} \\ \\ S_{30}=15(-155) \\ \\ S_{30}=-2,325 \end{gathered}[/tex]
The answer is -2,325.
