Answer
$a_6=-648$
Work Step by Step
To find the sixth term, the value of the common ratio $r$ is needed.
The value $r$ can be found by dividing the second term by the first term of the sequence.
Thus,
$r=\dfrac{a_2}{a}
\\r=\dfrac{-\frac{1}{2}}{\frac{1}{12}}
\\r=-\dfrac{1}{2} \cdot \dfrac{12}{1}
\\r=-\dfrac{12}{2}
\\r=-6$
The sixth term can be found by multiplying the common ratio $r$ to the second term four times:
$a_6 = a_2 \cdot r \cdot r \cdot r \cdot r
\\a_6=a_2 \cdot r^4
\\a_6 = -\dfrac{1}{2} \cdot (-6)^4
\\a_6 = -\dfrac{1}{2} \cdot 1296
\\a_6=-648$
