Answer
An equation for the $n^{th}$ term is $a_n=n-6$
and $a_{10}=4$
Work Step by Step
The given arithmetic sequence is
$-5,-4,-3,-2,...$
The first term $a_1=-5,$
and the common difference is $d=-4-(-5)=-4+5=1$
The $n^{th}$ term formula is
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $-5$ for $a_1$ and $1$ for $d$.
$\Rightarrow a_n=-5+(n-1)1$
Simplify.
$\Rightarrow a_n=-5+n-1$
$\Rightarrow a_n=n-6$
Substitute $10$ for $n$.
$\Rightarrow a_{10}=10-6$
Simplify.
$\Rightarrow a_{10}=4$.
