To solve this sequence, we need to find a pattern or rule that governs the progression of the numbers. Let's analyze the differences between consecutive terms:

1. \( 15 - 9 = 6 \)
2. \( 33 - 15 = 18 \)
3. \( 87 - 33 = 54 \)
4. \( 735 - 87 = 648 \)
5. \( 2193 - 735 = 1458 \)

We observe that the differences follow a pattern:

- \( 6 \times 3 = 18 \)
- \( 18 \times 3 = 54 \)
- \( 54 \times 3 = 162 \) (We can infer this for the missing number.)
- \( 162 \times 3 = 648 \)
- \( 648 \times 3 = 1458 \)

Thus, the missing number's difference from 87 should be 162. Adding this:

\[
87 + 162 = 249
\]

So, the missing number is **249**.

Let me know if you'd like further details on this solution!

Here are some related questions:
1. Can we apply the same multiplication pattern to other sequences?
2. How can we identify sequences with different growth rates?
3. Can sequences be solved using multiple patterns simultaneously?
4. How do we handle sequences where the pattern changes midway?
5. Can we generalize this approach for larger datasets?

**Tip:** Always check for common patterns like addition, multiplication, or alternating sequences when solving number progressions.

Learn how to solve the sequence 9, 15, 33, 87, ?, 735, 2193 by identifying the multiplication pattern in the differences of consecutive terms. This problem demonstrates arithmetic and geometric patterns suitable for students in Grades 6-8.

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