Let's analyze the sequence: **3, 6, 16, 24**.

To identify the pattern:

1. **First difference**:  
   6 - 3 = 3  
   16 - 6 = 10  
   24 - 16 = 8  

The differences are: **3, 10, 8**.

2. **Second difference**:  
   10 - 3 = 7  
   8 - 10 = -2  

The second differences vary: **7, -2**.

This suggests a possible non-linear pattern. One way to complete the sequence could be by extending these differences in a plausible way.

3. If we continue the second differences with a similar change, the next second difference could be **(-2 - 7 = -9)**, and adding this to the last first difference of 8:

   8 - 9 = -1 (next first difference)

4. Finally, adding this to the last term of the sequence:

   24 + (-1) = **23**

Thus, the next number in the pattern is **23**.

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Would you like more details or have any questions?  
Here are 5 questions that explore related ideas:

1. What if the differences between terms followed a geometric pattern?
2. Can you find a quadratic expression that fits this sequence?
3. How would the pattern change if the second differences were constant?
4. Can this sequence represent part of a function's values? If so, what function?
5. Could a missing term in the middle of a sequence be found using similar methods?

**Tip**: To identify patterns in sequences, try checking first and second differences to see if they follow a predictable rule.

Explore how to identify the pattern in the sequence 3, 6, 16, 24 by calculating first and second differences. Suitable for students in Grades 6-8, this problem demonstrates how to extend a non-linear sequence step-by-step.

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