The sequence you've provided is:

3, 5, 10, 18, 29, 43

Let's examine the differences between consecutive terms to identify the pattern:

- \( 5 - 3 = 2 \)
- \( 10 - 5 = 5 \)
- \( 18 - 10 = 8 \)
- \( 29 - 18 = 11 \)
- \( 43 - 29 = 14 \)

We notice that the differences between the terms form a secondary sequence: \( 2, 5, 8, 11, 14 \). This secondary sequence increases by 3 each time, meaning the differences between terms increase linearly.

Thus, the rule for generating the sequence is:
- Start with 3.
- Add an increasing difference, where the difference increases by 3 at each step.

Using this rule, the next term would be:
- \( 43 + (14 + 3) = 43 + 17 = 60 \).

So the next number in the sequence is 60.

Would you like more details on this, or do you have any other questions?

Here are 5 related questions to expand your understanding:

1. Can you find the 10th term in this sequence using the pattern?
2. How would you describe the nth term of this sequence using a formula?
3. Could you explore if the sequence follows any other kinds of patterns (e.g., quadratic)?
4. How could you prove that the differences between consecutive terms form an arithmetic sequence?
5. How does this sequence compare to other common sequences (like arithmetic or geometric)?

**Tip:** When identifying patterns in sequences, always check the differences between consecutive terms. The differences often reveal a hidden structure or rule.

Discover the pattern in the sequence 3, 5, 10, 18, 29, 43 by analyzing the increasing differences. Learn how the sequence follows an arithmetic progression with a stepwise increment, perfect for students in Grades 6-8.

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