Identify a pattern in the given list of numbers. Then use this pattern to find the next number.​ (More than one pattern might​ exist, so it is possible that there is more than one correct​ answer.)
8 , 15, 22, 29 ,36

Let's analyze the sequence \( 8, 15, 22, 29, 36 \) to identify a pattern and determine the next number.

### Step 1: Find the differences between consecutive terms.

- Difference between \( 15 \) and \( 8 \): \( 15 - 8 = 7 \)
- Difference between \( 22 \) and \( 15 \): \( 22 - 15 = 7 \)
- Difference between \( 29 \) and \( 22 \): \( 29 - 22 = 7 \)
- Difference between \( 36 \) and \( 29 \): \( 36 - 29 = 7 \)

### Step 2: Identify the pattern.
The differences between consecutive terms are constant at \( 7 \). This suggests an **arithmetic sequence** where each term is obtained by adding 7 to the previous term.

### Step 3: Find the next number in the sequence.
Since the pattern is to add 7 to the previous term:

\[
36 + 7 = 43
\]

### Conclusion:
The next number in the sequence is **43**.

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

Here are some related questions:
1. How do arithmetic sequences differ from geometric sequences?
2. What is the formula for the \( n \)-th term of an arithmetic sequence?
3. Can this sequence be extended to an infinite series?
4. How would the sequence change if the common difference were negative?
5. What are some real-world applications of arithmetic sequences?

**Tip:** Recognizing constant differences in sequences can quickly help identify arithmetic patterns. This is useful in many mathematical contexts, from simple number puzzles to advanced financial calculations.

Learn how to identify the pattern in the sequence 8, 15, 22, 29, 36 and find the next number using arithmetic sequence principles. This problem explores constant differences between terms and applies the formula for the n-th term of an arithmetic sequence. Suitable for students in Grades 7-9.

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