Recall that in a geometric sequence, whenever we take one value of the sequence and divide it by the next number of the sequence, we would get a constant number unique to that sequence. If we take the first and second numbers and calculate the ratio, we get
[tex]\frac{x}{3}[/tex]
if we do that with the second and third numbers, we get
[tex]\frac{3}{\text{ -}\frac{1}{3}}=\text{ -}\frac{3\cdot3}{1\cdot1}=\text{ -9}[/tex]
this two numbers should be equal. So we get
[tex]\frac{x}{3}=\text{ -9}[/tex]
if we multiply both sides by 3, we get
[tex]x=3\cdot\text{ -9= -27}[/tex]
so option A is the correct option.
