Answer
An equation for the $n^{th}$ term is
$a_n=-n+2$
and
$a_{25}=-23$
Work Step by Step
The given arithmetic sequence is
$1,0,-1,-2,...$
The first term $a_1=1,$
and the common difference is $d=0-1=-1$
The $n^{th}$ term formula is
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $1$ for $a_1$ and $-1$ for $d$.
$\Rightarrow a_n=1+(n-1)(-1)$
Simplify.
$\Rightarrow a_n=1-n+1$
$\Rightarrow a_n=-n+2$
Substitute $25$ for $n$.
$\Rightarrow a_{25}=-25+2$
Simplify.
$\Rightarrow a_{25}=-23$.
