The given sequence is: **12, 42, 48, 69, ?**

Let's analyze the differences between consecutive terms:

1. \( 42 - 12 = 30 \)
2. \( 48 - 42 = 6 \)
3. \( 69 - 48 = 21 \)

So, the differences between consecutive terms are 30, 6, and 21. These differences don't follow a simple arithmetic or geometric pattern, but we can notice that they might follow an alternating pattern:

1. \( 30 = 5 \times 6 \)
2. \( 6 = 1 \times 6 \)
3. \( 21 = 3 \times 7 \)

If this alternating pattern holds, the next difference could be a multiple of 1 again. 

Let’s try adding **6** to the last term (69):
\[ 69 + 6 = 75 \]

Thus, the next number in the sequence is likely **75**.

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Would you like further details or have any questions?

Here are 5 related questions to expand this:
1. Can you identify other types of sequences (e.g., geometric)?
2. How can you check if a sequence is arithmetic?
3. What happens if you change the first term in this sequence?
4. Could this sequence be interpreted as part of a real-world problem?
5. How do factorials or primes influence sequences?

**Tip:** Always check for alternating patterns in sequences—they may provide clues when standard methods don't apply!

Explore the number sequence 12, 42, 48, 69, and find the next term in the series by identifying patterns. This problem helps students practice sequence recognition and alternating patterns. Suitable for students in Grades 5-7.

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