Let's analyze the sequence \(15, 16, 18, 21, \ldots\).

To find the pattern, we can look at the differences between consecutive terms:

- \(16 - 15 = 1\)
- \(18 - 16 = 2\)
- \(21 - 18 = 3\)

The differences are \(1, 2, 3\), which form an increasing sequence. It appears that the difference between consecutive terms increases by 1 each time.

To continue the pattern, the next difference should be \(4\):

- \(21 + 4 = 25\)

Continuing with the next difference \(5\):

- \(25 + 5 = 30\)

Continuing with the next difference \(6\):

- \(30 + 6 = 36\)

So, the next terms in the sequence are \(25, 30, 36\).

Thus, the sequence is: \(15, 16, 18, 21, 25, 30, 36, \ldots\)

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

1. How can you express the general term of this sequence?
2. What is the sum of the first \(n\) terms of this sequence?
3. Can you find a recursive formula for this sequence?
4. How does the pattern of differences help in identifying the sequence type?
5. What is the 10th term in this sequence?
6. Can you represent this sequence graphically and analyze its growth?
7. How does the concept of arithmetic sequences relate to this pattern?
8. How do the differences between terms evolve as the sequence progresses?

**Tip:** When analyzing a sequence, looking at the differences between terms can often reveal the underlying pattern.

Explore the sequence 15, 16, 18, 21, ... with detailed analysis and pattern recognition. Discover how differences between terms reveal the underlying arithmetic sequence pattern. Suitable for students in Grades 9-12.

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