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The given sequence is \( 3, 6, 9, 12, \dots \). This sequence increases by 3 each time, indicating that it is an arithmetic sequence with a common difference of 3.

To write the recursive formula:

- The first term \( a_1 = 3 \).
- The recursive relationship for an arithmetic sequence is \( a_n = a_{n-1} + d \), where \( d \) is the common difference.
- In this case, the common difference \( d = 3 \).

Thus, the recursive formula is:

\[
a_1 = 3, \quad a_n = a_{n-1} + 3 \text{ for } n \geq 2.
\]

Looking at the answer choices in the image:

- The blue option (top right) shows the correct recursive formula: \( a_1 = 3 \) and \( a_n = a_{n-1} + 3 \).

Would you like more details or have any questions about this? Here are some related questions:

1. What is the explicit formula for this sequence?
2. How can you identify the common difference in an arithmetic sequence?
3. What are the next three terms in this sequence?
4. How does a recursive formula differ from an explicit formula?
5. Can this recursive formula be applied to geometric sequences as well?

**Tip:** In a recursive formula, each term depends on the previous one, while an explicit formula allows you to find any term directly.

Write the recursive formula for the sequence 3, 6, 9, 12, ...

Learn how to write the recursive formula for the arithmetic sequence 3, 6, 9, 12. This problem introduces key concepts in arithmetic sequences, recursion, and sequence formulas. Suitable for students in Grades 6-8.

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