Question

What is the sum of the first 14 terms of the sequence? -11+ (-18) + (-25) + (-32) + ...

Answer 1

First, we are going to find the difference,
`d`, of our sequence. Remember that in an arithmetic sequence
`d=a_(n)-a_(n-1)`, so:

`d=-18-(-11)`

`d=-18+11`

`d=-7`

Now that we have our difference, we can find the sum of the first 14 terms of our sequence using the formula:
`S_(n)= (n)/(2) [2a_(1)+(n-1)d]`
where

`n` is the number of terms we want to add

We now know that
`a_(1)=-11`,
`d=-7`, and
`n=14`. So lets replace those values in our formula:

`S_(n)= (14)/(2) [2(-11)+(14-1)(-7)]`

`S_(n)=7[-22+(13)(-7)]`

`S_(n)=7(-22-91)`

`S_(n)=7(-113)`

`S_(n)=-791`

We can conclude that the sum of the first 14 terms of our sequence is -791.