https://file.aiquickdraw.com/mathbot/file/1729532747980sq3h8dne.jpg

The sequence provided is: \( 3, 6, 12, 24, \dots \). 

The numbers in this sequence are doubling each time: 
- \( 6 = 2 \times 3 \)
- \( 12 = 2 \times 6 \)
- \( 24 = 2 \times 12 \)

This indicates that the recursive formula involves multiplying the previous term by 2.

The recursive formula for this sequence is:
\[
a_1 = 3; \quad a_n = 2a_{n-1} \text{ for } n \geq 2.
\]
This corresponds to the yellow box in the image.

Do you want further details or have any questions?

Here are 5 related questions:
1. What is the next term in the sequence after 24?
2. How would you describe the general formula for this sequence without recursion?
3. Can you create a recursive formula for a sequence where the terms triple each time?
4. What is the difference between recursive and explicit formulas?
5. How would the sequence change if you multiplied by 3 instead of 2?

**Tip:** Recursive formulas express each term based on the previous one, making them powerful for sequences that follow a clear pattern.

Write the recursive formula for the sequence: 3, 6, 12, 24,...

Learn how to find the recursive formula for the geometric sequence 3, 6, 12, 24,... This problem involves recursion and geometric progression, key concepts in algebra. Suitable for students in Grades 8-10.

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