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The table you've provided contains two rows of numbers. Let's analyze the structure of this sequence:

- Top row: 9, 18, 27, 36, 45
- Bottom row: 15, 30, 45, 60, 75

These two rows appear to be arithmetic progressions, where each number in the sequence increases by a constant difference.

### Top Row (9, 18, 27, 36, 45):
- The difference between consecutive numbers is 9.
- This suggests an arithmetic progression with a common difference of 9.

### Bottom Row (15, 30, 45, 60, 75):
- The difference between consecutive numbers is 15.
- This suggests an arithmetic progression with a common difference of 15.

It seems the sequence in each row is a simple arithmetic progression where each number in the second row is \( 1.67 \) times (or approximately \(\frac{5}{3}\)) the corresponding number in the first row.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the formula for finding the \(n\)-th term of an arithmetic progression?
2. Can you generalize a rule for comparing corresponding numbers in both rows?
3. How do you calculate the sum of an arithmetic progression?
4. How could this pattern be extended to additional terms?
5. What would be the common difference in an arithmetic progression if the difference between two consecutive terms was not constant?

**Tip:** In arithmetic sequences, the common difference helps define the entire progression, so identifying it early simplifies solving problems!

The user provided a table containing two rows of numbers: Top row (9, 18, 27, 36, 45) and Bottom row (15, 30, 45, 60, 75). The goal is to analyze the patterns in the sequences.

Explore arithmetic progressions using the sequences 9, 18, 27, 36, 45 and 15, 30, 45, 60, 75. Learn how to identify the common difference and find the nth term of each sequence. Suitable for students in Grades 6-8.

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