2) Find the next three terms of each sequence.


b) 225, 45, 9, 1.8,...

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.

2) Find the next three terms of each sequence.
b) 225, 45, 9, 1.8,...

Learn how to find the next three terms of the geometric sequence starting with 225, 45, 9, 1.8. This problem explores key concepts in geometric sequences, including calculating the common ratio and using it to predict future terms. Suitable for students in Grades 6-8.

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