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The given sequence is:

\[ 3, 6, 9, 15, 30, 45, 75, \dots \]

We need to determine the next number in the sequence.

### Analyzing the sequence:
- **First difference:**  
  \( 6 - 3 = 3 \)  
  \( 9 - 6 = 3 \)  
  \( 15 - 9 = 6 \)  
  \( 30 - 15 = 15 \)  
  \( 45 - 30 = 15 \)  
  \( 75 - 45 = 30 \)

So, the differences between the terms are:
\[ 3, 3, 6, 15, 15, 30 \]

From this, it appears the differences increase irregularly, but a pattern may be emerging where larger numbers start to increase.

### Predicting the next number:
Following the pattern in the differences, it is likely the next difference will be:
\[ 30 + 15 = 45 \]

So, the next term would be:
\[ 75 + 45 = 120 \]

Thus, the next number in the sequence is **120**.

Would you like more details on this or any other questions? Here are some related questions:

1. How do you find patterns in number sequences?
2. Can you explain arithmetic vs geometric sequences?
3. How do increasing differences affect sequence progression?
4. What is the difference between a linear and non-linear sequence?
5. What are some common types of number sequences?

**Tip:** Always look for changes in the differences between terms when faced with complex sequences!

What is the next number in the sequence 3, 6, 9, 15, 30, 45, 75, ...?

Learn how to find the next number in the sequence 3, 6, 9, 15, 30, 45, 75 using a pattern in the differences between consecutive terms. Suitable for students in Grades 6-8.

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