ANSWER
-3
EXPLANATION
The formula for the general term of a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]In this sequence the first term a1 = -2. With this and the second term a2 = 6 we can find the common ratio and then verify with the next terms:
[tex]\begin{gathered} a_2=a_1\cdot r^{2-1} \\ a_2=a_1\cdot r \\ r=\frac{a_2}{a_1} \\ r=\frac{6}{-2} \\ r=-3 \end{gathered}[/tex]If we use this common ratio to find the 3rd and 4th terms we have to arrive to the same result as the given sequence:
[tex]\begin{gathered} a_3=-2\cdot(-3)^2 \\ a_3=-2\cdot9 \\ a_3=-18\to OK \end{gathered}[/tex][tex]\begin{gathered} a_4=-2\cdot(-3)^3 \\ a_4=-2\cdot(-27) \\ a_4=54\to OK \end{gathered}[/tex]The common ratio of this sequence is -3
