Answer
An equation for the $n^{th}$ term is $a_n=10n+90$
and $a_{10}=190$
Work Step by Step
The given arithmetic sequence is
$100,110,120,130,...$
The first term $a_1=100,$
and the common difference is $d=110-100=10$
The $n^{th}$ term formula is
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $100$ for $a_1$ and $1$ for $10$.
$\Rightarrow a_n=100+(n-1)(10)$
Simplify.
$\Rightarrow a_n=100+10n-10$
$\Rightarrow a_n=10n+90$
Substitute $10$ for $n$.
$\Rightarrow a_{10}=10(10)+90$
Simplify.
$\Rightarrow a_{10}=100+90$
$\Rightarrow a_{10}=190$.
