https://file.aiquickdraw.com/mathbot/file/1726537256487idppwohm.jpg

We are given an arithmetic sequence:  
\[
-15, -11, -7, -3, \dots
\]

To write the recursive formula, let's break it down:

1. The first term of the sequence is \( c(1) \). In this case, the first term is \( -15 \). Therefore:
   \[
   c(1) = -15
   \]

2. In an arithmetic sequence, the difference between consecutive terms (common difference) is constant. Let's calculate the common difference (\(d\)) by subtracting the first term from the second term:
   \[
   d = -11 - (-15) = 4
   \]
   Therefore, the common difference is \(4\).

3. The recursive formula for an arithmetic sequence is given by:
   \[
   c(n) = c(n-1) + d
   \]
   Since \(d = 4\), the recursive formula becomes:
   \[
   c(n) = c(n-1) + 4
   \]

So, the completed recursive formula is:
- \( c(1) = -15 \)
- \( c(n) = c(n-1) + 4 \)

Let me know if you need further clarification or details!

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Here are five related questions to further your understanding:
1. What is the 10th term of the arithmetic sequence?
2. How would you write the explicit formula for this arithmetic sequence?
3. Can you find the sum of the first 20 terms of this sequence?
4. How does the recursive formula change if the common difference were negative?
5. What is the general form of a recursive formula for any arithmetic sequence?

**Tip:** To find any term in an arithmetic sequence, you can use the explicit formula: \( c(n) = c(1) + (n-1) \times d \).

Complete the recursive formula of the arithmetic sequence -15, -11, -7, -3, ...

Learn how to complete the recursive formula for the arithmetic sequence -15, -11, -7, -3. Understand key concepts like common difference, recursive formulas, and how to find future terms in the sequence. Ideal for students in Grades 7-9.

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