Answer
The equation for the $n$th term is
$a_n=0.1(9)^{n-1}$
and $a_6=5904.9$
Work Step by Step
The given series is
$0.1,0.9,8.1,72.9,...$
First term $a_1=0.1$.
Common ratio $r=\frac{0.9}{0.1}=9$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $0.1$ for $a_1$ and $9$ for $r$.
$\Rightarrow a_n=0.1(9)^{n-1}$
Substitute $6$ for $n$.
$\Rightarrow a_6=0.1(9)^{6-1}$
Simplify.
$\Rightarrow a_6=0.1(9)^{5}$
$\Rightarrow a_6=5904.9$.
