Question

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

Answer 1

Answer:  The required common ratio for the given geometric sequence is $\dfrac{1}{5}.$

Step-by-step explanation:  We are given to find the common ratio for the following geometric sequence :

225,   45,   9,   .   .   .

We know that

in a geometric sequence, the ratio of any term with the preceding term is the common ratio of the sequence.

For the given geometric sequence, we have

a(1) = 225,  a(2) = 45,   a(3) = 9,  etc.

So, the common ratio (r) is given by

$r=\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=~~.~~.~~.~~.$

We have

$\dfrac{a(2)}{a(1)}=\dfrac{45}{225}=\dfrac{1}{5},\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{9}{45}=\dfrac{1}{5},~etc.$

Therefore, we get

$r=\dfrac{1}{5}.$

Thus, the required common ratio for the given geometric sequence is $\dfrac{1}{5}.$

Answer 2

The common ratio is 1/5