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: $S_{n}= \frac{n}{2} [2a_{1}+(n-1)d]$ 
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:
$S_{n}= \frac{14}{2} [2(-11)+(14-1)(-7)]$
$S_{n}=7[-22+(13)(-7)]$
$S_{n}=7(-22-91)$
$S_{n}=7(-113)$
$S_{n}=-791$

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