Question

Given the following geometric sequence, find the common ratio: {225, 45, 9...}

Answer 1

Answer:

$\frac{1}{5}$  is the common ratio

Step-by-step explanation:

Common ratio(r) states that the ratio of each term of a geometric sequence to the term preceding it.

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

Given the sequence:

225, 45, 9, .........

Here,

$a_1 = 225$

$a_2 = 45$

$a_3 = 9$ and so on...

Using definition to find r.

$r = \frac{45}{225}=\frac{9}{45}......$

After solving we get;

$r = \frac{1}{5}$

Therefore, the common ratio is, $\frac{1}{5}$

Answer 2

Answer:

$r=\frac{1}{5}$

Step-by-step explanation:

We are given that a geometric sequence

225,45,9,...

We have to find the common ratio of the geometric sequence.

$a=225,a_2=45,a_3=9$

$r=\frac{a_2}{a_1}$

$a_2=ar$

Substitute the values then we get

$45=225r$

$r=\frac{45}{225}$

$r=\frac{1}{5}$

Hence, the common ratio of the geometric sequence =$\frac{1}{5}$