Answer
$S_{10}=-46.25$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find $S_{10}$ in the given sequence
\begin{array}{l}\require{cancel}
a_1=-8, a_{10}=-1.25
\end{array}
use the formula for finding the sum of the first $n$ terms of an arithmetic sequence.
$\bf{\text{Solution Details:}}$
Using the formula for the sum of the first $n$ terms of an airthmetic sequence, which is given by $
S_n=\dfrac{n}{2}[a_1+a_n]
,$ then the sum of the first $n=10$ terms with $a_1=-8$ and $a_{n}=-1.25$ is
\begin{array}{l}\require{cancel}
S_n=\dfrac{n}{2}[a_1+a_n]
\\\\
S_{10}=\dfrac{10}{2}[-8+(-1.25)]
\\\\
S_{10}=\dfrac{10}{2}[-8-1.25]
\\\\
S_{10}=5[-9.25]
\\\\
S_{10}=-46.25
.\end{array}
