Let's analyze the given sequence: $225, 45, 9, 1.8, \dots$.

Each term is being divided by the same number to get the next term, which suggests this is a geometric sequence. To find the common ratio, divide the second term by the first term:

$r = \frac{45}{225} = 0.2$

So, the common ratio is $0.2$. Now, we can find the next three terms by multiplying each term by $0.2$.

1. The next term after $1.8$ is: $1.8 \times 0.2 = 0.36$

2. The term after $0.36$ is: $0.36 \times 0.2 = 0.072$

3. The term after $0.072$ is: $0.072 \times 0.2 = 0.0144$

Thus, the next three terms are: $0.36, 0.072, 0.0144$.

Would you like more details on this solution or have any questions?

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Here are five questions to expand on this topic:

1. What is a geometric sequence, and how is it different from an arithmetic sequence?
2. How do you find the common ratio in a geometric sequence?
3. Can you find the sum of an infinite geometric sequence? Under what conditions is this possible?
4. What is the formula for the $n$-th term of a geometric sequence?
5. How would the sequence change if the common ratio were negative?

Tip: In geometric sequences, the common ratio can be found by dividing any term by the previous one, ensuring consistent progression.