Question

The second term in a geometric sequence is 12. The fourth term in the same sequence is 4/3. What is the common ratio in this sequence?

Answer 1

The common ratio in this sequence is 6:2 or 4:3

Answer 2

Answer:

The common ratio is $r=\pm\frac{1}{3}$.

Step-by-step explanation:

Given : The second term in a geometric sequence is 12. The fourth term in the same sequence is 4/3.

To find : What is the common ratio in this sequence?

Solution :

The nth term of G.P is $a_n=ar^{n-1}$

The second term in a geometric sequence is 12.

i.e. $a_2=ar^{2-1}$

$12=ar$ .....(1)

The four term in a geometric sequence is $\frac{4}{3}$.

i.e. $a_4=ar^{4-1}$

$\frac{4}{3}=ar^3$ .....(2)

Divide (1) and (2),

$\frac{\frac{4}{3}}{12}=\frac{ar^3}{ar}$

$\frac{1}{9}=r^2$

$\sqrt{\frac{1}{9}}=r$

$\pm\frac{1}{3}=r$

Therefore, the common ratio is $r=\pm\frac{1}{3}$.