First, we are going to find the difference, [tex]d[/tex], of our sequence. Remember that in an arithmetic sequence [tex]d=a_{n}-a_{n-1}[/tex], so:
[tex]d=-18-(-11)[/tex]
[tex]d=-18+11[/tex]
[tex]d=-7[/tex]
Now that we have our difference, we can find the sum of the first 14 terms of our sequence using the formula: [tex]S_{n}= \frac{n}{2} [2a_{1}+(n-1)d][/tex]
where
[tex]n[/tex] is the number of terms we want to add
We now know that [tex]a_{1}=-11[/tex], [tex]d=-7[/tex], and [tex]n=14[/tex]. So lets replace those values in our formula:
[tex]S_{n}= \frac{14}{2} [2(-11)+(14-1)(-7)][/tex]
[tex]S_{n}=7[-22+(13)(-7)][/tex]
[tex]S_{n}=7(-22-91)[/tex]
[tex]S_{n}=7(-113)[/tex]
[tex]S_{n}=-791[/tex]
We can conclude that the sum of the first 14 terms of our sequence is -791.
