Answer
$\frac{1}{9}$.
Work Step by Step
The given series is
$81,27,9,3,1,...$
First term $a=81$.
Common ratio $r=\frac{27}{81}=\frac{1}{3}$.
The formula for the $n^{th}$ term is
$\Rightarrow a_n=a(r)^{n-1}$
Substitute all values.
$\Rightarrow a_7=81(\frac{1}{3})^{7-1}$
Simplify.
$\Rightarrow a_7=81(\frac{1}{3})^{6}$
$\Rightarrow a_7=\frac{1}{9}$.
