Question

The first four terms of a geometric sequence are 108, 36, 12, 4, … What is the common ratio?
–72
–3
3
1/3

Answer 1

The first four terms of a geometric sequence are 108, 36, 12, 4, … What is the common ratio?
–72
–3
3
☆☆☆☆☆☆☆☆1/3

Answer 2

Answer:

Option 4th is correct

$\frac{1}{3}$

Step-by-step explanation:

Common ratio(r) defined as the ratio of a term to the previous term.

$r = \frac{a_2}{a_1} = \frac{a_3}{a_2}......................\frac{a_{n+1}}{a_n}$

As per the statement:

The first four terms of a geometric sequence are

108, 36, 12, 4, …

Here,

$a_1 = 108$

$a_2 = 36$

$a_3 = 12$

$a_4 = 4$ and so on...

We have to find the common ratio.

By definition we have;

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

Since;

$r = \frac{36}{108} =\frac{12}{36}=\frac{4}{12}.........=\frac{1}{3}$

Therefore, the common ratio is, $\frac{1}{3}$