ANSWER
[tex]r=-6[/tex]EXPLANATION
We want to find the common ratio of the geometric sequence.
[tex]-2,12,-72[/tex]To do this, divide a term by its preceeding term.
Let us divide 12 by -2 and -72 by 12:
That is:
[tex]\begin{gathered} \Rightarrow r=\frac{12}{-2} \\ r=-6 \\ \Rightarrow r=\frac{-72}{12} \\ r=-6 \end{gathered}[/tex]The common ratio is 6.