Question

what is the common ratio of the geometic sequence whose second and forth terms are 6 and 54, respectively?

a) 1
b) 2
c) 3
d) 4​

Answer 1

Answer:

C

Step-by-step explanation:

The n th term formula of a geometric sequence is

$a_{n}$ = a $r^{n-1}$

where a is the first term and r the common ratio

Using the second and fourth term, then

ar = 6 → (1)

ar³ = 54 → (2)

Divide (2) by (1)

$\frac{ar^3}{ar}$ = $\frac{54}{6}$ = 9

r² = 9 ⇒ r = $\sqrt{9}$ = 3 → C

Answer 2

The answer would be C.