Answer
The equation for the $n$th term is
$a_n=0.6(-5)^{n-1}$
and $a_6=-1875$
Work Step by Step
The given series is
$0.6,-3,15,-75,...$
First term $a_1=0.6$.
Common ratio $r=\frac{-3}{0.6}=-5$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $0.6$ for $a_1$ and $-5$ for $r$.
$\Rightarrow a_n=0.6(-5)^{n-1}$
Substitute $6$ for $n$.
$\Rightarrow a_6=0.6(-5)^{6-1}$
Simplify.
$\Rightarrow a_6=0.6(-5)^{5}$
$\Rightarrow a_6=-1875$.
