Answer
$a_5 = -512$
$a_n=-2 \cdot 4^{n-1}$
Work Step by Step
RECALL:
The $n^{th}$ term $a_n$ of a geometric sequence is given by the formula
$a_n=a_1 \cdot r^{n-1}$
where
$a_1$ = first term
$r$ = common ratio
The given geometric sequence has:
$a_1=-2$
$r=4$
Thus, the $n^{th}$ term of the sequence is given by the formula:
$a_n = -2 \cdot 4^{n-1}$
The 5th term can be found by substituting $5$ for $n$:
$a_5=-2 \cdot 4^{5-1}
\\a_5=-2 \cdot 4^4
\\a_5 = -2(256)
\\a_5 = -512$
