Identify the pattern in the list of numbers. Then use this pattern to find the next number.
3, 6, 9, 15, 24, 39,
Fill in the next number in the list.

Let's identify the pattern in the sequence:

The sequence is: 3, 6, 9, 15, 24, 39.

We can find the difference between consecutive terms:

- \(6 - 3 = 3\)
- \(9 - 6 = 3\)
- \(15 - 9 = 6\)
- \(24 - 15 = 9\)
- \(39 - 24 = 15\)

The differences between the terms form this sequence: 3, 3, 6, 9, 15.

Now, observe that the differences are increasing as follows:

- \(3, 6, 9, 15\), which suggests that the next difference could be \(15 + 6 = 21\).

Therefore, to find the next number, we add 21 to the last term in the sequence:

\[
39 + 21 = 60
\]

Thus, the next number in the sequence is **60**.

Would you like more details or have any questions?

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Here are 5 related questions to explore this further:
1. What would the 8th term in this sequence be?
2. Can you find a formula to express the \(n\)-th term in this sequence?
3. What kind of sequences have non-constant differences?
4. How would you extend this pattern to find the 20th term?
5. How does this sequence differ from an arithmetic progression?

**Tip:** When differences between terms form a sequence themselves, this may suggest an additive or recursive pattern.

Identify the pattern in the list of numbers. Then use this pattern to find the next number. 3, 6, 9, 15, 24, 39, Fill in the next number in the list.

Learn how to find the next number in the sequence 3, 6, 9, 15, 24, 39 by identifying a recursive pattern in the differences between consecutive terms. This problem is suitable for students in Grades 6-8 and covers key concepts in number patterns and arithmetic sequences.

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