Question

What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54, respectively?

Answer 1

Answer:

C

Step-by-step explanation:

For a geometric sequence the n th term is

$a_{n}$ = $a_{1}$$r^{n-1}$, hence

$a_{2}$ = $a_{1}$ r = 6 → (1)

$a_{4}$ = $a_{1}$$r^{3}$ = 54 → (2)

divide (2) by (1) cancelling $a_{1}$, hence

$\frac{r^{3} }{r}$ = $\frac{54}{6}$

hence $r^{2}$ = 9 ( take the square root of both sides )

r = 3 → C