Answer
An equation for the $n^{th}$ term is $a_n=-10n+20$
and $a_{10}=-80$
Work Step by Step
The given arithmetic sequence is
$10,0,-10,-20,...$
The first term $a_1=10,$
and the common difference is $d=0-10=-10$
The $n^{th}$ term formula is
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $10$ for $a_1$ and $1$ for $-10$.
$\Rightarrow a_n=10+(n-1)(-10)$
Simplify.
$\Rightarrow a_n=10-10n+10$
$\Rightarrow a_n=-10n+20$
Substitute $10$ for $n$.
$\Rightarrow a_{10}=-10(10)+20$
Simplify.
$\Rightarrow a_{10}=-100+20$
$\Rightarrow a_{10}=-80$.
