https://file.aiquickdraw.com/mathbot/file/1726442545734l1hy8iwn.jpg

Let's analyze the sequences given in the image and solve for the common difference, followed by the recursive formulas:

### 1. Sequence: \(-39, -33, -27, -21, \dots\)
   - **Common Difference (d)**: 
     \( -33 - (-39) = 6 \)
   - **Recursive Formula**: 
     \( a_n = a_{n-1} + 6 \)

### 2. Sequence: \( 17, 13, 9, 5, \dots \)
   - **Common Difference (d)**: 
     \( 13 - 17 = -4 \)
   - **Recursive Formula**: 
     \( a_n = a_{n-1} - 4 \)

### 3. Sequence: \( 9, 19, 29, 39, \dots \)
   - **Common Difference (d)**: 
     \( 19 - 9 = 10 \)
   - **Recursive Formula**: 
     \( a_n = a_{n-1} + 10 \)

### 4. Sequence: \( -3, 97, 197, 297, \dots \)
   - **Common Difference (d)**: 
     \( 97 - (-3) = 100 \)
   - **Recursive Formula**: 
     \( a_n = a_{n-1} + 100 \)

Would you like further details or explanations?

Here are some related questions to expand your understanding:
1. How can you identify an arithmetic sequence from its terms?
2. What is the general formula for the \(n\)-th term in an arithmetic sequence?
3. How does the recursive formula differ from the explicit formula of an arithmetic sequence?
4. Can you apply this method to geometric sequences?
5. What are some real-life applications of arithmetic sequences?

**Tip**: Always check the first two terms of a sequence to determine the common difference; this helps in writing the recursive formula!

Find the common difference and write the recursive formula for the arithmetic sequences provided.

Explore how to find the common difference and write recursive formulas for arithmetic sequences. Example sequences include (-39, -33, -27, -21, ...), (17, 13, 9, 5, ...), and others. Perfect for students in Grades 7-9.

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