Answer
$S_{8} = 20$
Work Step by Step
In order to find the sum of this finite series, we need to find the first term, $a_{1}$ and the last term, $a_{8}$.
First, use the explicit formula given and plug in $1$ for $n$ to find $a_{1}$:
$a_{1} = 7 - 1$
Subtract:
$a_{1} = 6$
Use the explicit formula and plug in $8$ for $n$ to find $a_{8}$:
$a_{8} = 7 - 8$
Subtract:
$a_{8} = -1$
Plug the two values just found into the formula for the sum of a finite arithmetic series, which is given by $S_{n} = \frac{n}{2}(a_{1} + a_{n})$, to find the sum of the series:
$S_{8} = \frac{8}{2}(6 + (-1))$
Evaluate what is inside the parentheses first:
$S_{8} = \frac{8}{2}(5)$
Multiply:
$S_{8} = \frac{40}{2}$
Simplify the fraction:
$S_{8} = 20$