Question

Hello,Can you please help me with question 27 in the picture?Thank you,

Answer 1

To find the sum of the first n terms of an arithmetic sequence, we use the formula (which you also gave):

`S_n=(n(a_1+a_n))/(2)`

Let's find a1 first by substituting 1 for i.

`\begin{gathered} a_i=-5i \\ a_1=-5(1) \\ a_1=-5 \end{gathered}`

Next, let's solve for the last term, a30.

`\begin{gathered} a_(30)=-5(30) \\ a_(30)=-150 \end{gathered}`

Let's use these values to solve for the sum.

`\begin{gathered} S_(30)=(30[-5+(-150)])/(2) \\ \\ S_(30)=(30(-155))/(2) \\ \\ S_(30)=15(-155) \\ \\ S_(30)=-2,325 \end{gathered}`

The answer is -2,325.