Answer:
[tex]\frac{1}{5}[/tex] 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.
[tex]r = \frac{a_2}{a_1} =\frac{a_3}{a_2}........\frac{a_{n+1}}{a_n}[/tex]
Given the sequence:
225, 45, 9, .........
Here,
[tex]a_1 = 225[/tex]
[tex]a_2 = 45[/tex]
[tex]a_3 = 9[/tex] and so on...
Using definition to find r.
[tex]r = \frac{45}{225}=\frac{9}{45}......[/tex]
After solving we get;
[tex]r = \frac{1}{5}[/tex]
Therefore, the common ratio is, [tex]\frac{1}{5}[/tex]
Answer:
[tex]r=\frac{1}{5}[/tex]
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.
[tex]a=225,a_2=45,a_3=9[/tex]
[tex]r=\frac{a_2}{a_1}[/tex]
[tex]a_2=ar[/tex]
Substitute the values then we get
[tex]45=225r[/tex]
[tex]r=\frac{45}{225}[/tex]
[tex]r=\frac{1}{5}[/tex]
Hence, the common ratio of the geometric sequence =[tex]\frac{1}{5}[/tex]
