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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, \(\frac{1}{5}\)

lublana

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 =\(\frac{1}{5}\)

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