Answer
The equation for the $n$th term is
$a_n=-192(-\frac{1}{4})^{n-1}$
and $a_6=0.1875$
Work Step by Step
Write down the series from the table.
$-192,48,-12,3,...$
First term $a_1=-192$.
Common ratio $r=\frac{48}{-192}=-\frac{1}{4}$.
Equation for a geometric sequence is
$\Rightarrow a_n=a_1r^{n-1}$
Substitute $-192$ for $a_1$ and $-\frac{1}{4}$ for $r$.
$\Rightarrow a_n=-192(-\frac{1}{4})^{n-1}$
Substitute $6$ for $n$.
$\Rightarrow a_6=-192(-\frac{1}{4})^{6-1}$
Simplify.
$\Rightarrow a_6=-192(-\frac{1}{4})^{5}$
$\Rightarrow a_6=0.1875$.
