Answer
An equation for the $n^{th}$ term is $a_n=-3n-3$ and $a_{10}=-33$
Work Step by Step
The given arithmetic sequence is
$-6,-9,-12,-15,...$
The first term $a_1=-6,$
and the common difference is $d=-9-(-6)=-9+6=-3$
The $n^{th}$ term formula is
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $-6$ for $a_1$ and $1$ for $-3$.
$\Rightarrow a_n=-6+(n-1)(-3)$
Simplify.
$\Rightarrow a_n=-6-3n+3$
$\Rightarrow a_n=-3n-3$
Substitute $10$ for $n$.
$\Rightarrow a_{10}=-3(10)-3$
Simplify.
$\Rightarrow a_{10}=-30-3$
$\Rightarrow a_{10}=-33$.
