#### Answer

$r = -0.3$
$a_5=0.00243$
The $n^{th}$ term of the geometric sequence is: $a_n=0.3 \cdot \left(-0.3\right)^{n-1}$

#### Work Step by Step

RECALL:
(1) The common ratio of a geometric sequence is equal to the quotient of any two consecutive terms:
$r =\dfrac{a_n}{a_{n-1}}$
(2) The $n^{th}$ term of a geometric sequence is given by the formula:
$a_n = a\cdot r^{n-1}$
where
$a$ = first term
$r$ = common ratio
The sequence is said to be geometric.
Thus, we can proceed to solving for the common ratio:
$r=\dfrac{-0.09}{0.3}
\\r = -0.3$
The fifth term can be found by multiplying the common ratio to the fourth term.
The fourth term is $-0.0081$.
Thus, the fifth term is:
$a_5=-0.0081 \cdot -0.3
\\a_5=0.00243$
With a first term of $0.3$ and a common ratio of $r=-0.3$, the $n^{th}$ term of the geometric sequence is:
$a_n=a \cdot r^{n-1}
\\a_n=0.3 \cdot \left(-0.3\right)^{n-1}$