Answer:
C
Step-by-step explanation:
For a geometric sequence the n th term is
[tex]a_{n}[/tex] = [tex]a_{1}[/tex][tex]r^{n-1}[/tex], hence
[tex]a_{2}[/tex] = [tex]a_{1}[/tex] r = 6 → (1)
[tex]a_{4}[/tex] = [tex]a_{1}[/tex][tex]r^{3}[/tex] = 54 → (2)
divide (2) by (1) cancelling [tex]a_{1}[/tex], hence
[tex]\frac{r^{3} }{r}[/tex] = [tex]\frac{54}{6}[/tex]
hence [tex]r^{2}[/tex] = 9 ( take the square root of both sides )
r = 3 → C
