The numbers you've listed form a sequence: 16, 24, 36, 54.

Let's analyze the sequence:

### Common Ratio/Pattern
- From 16 to 24, the difference is \(24 - 16 = 8\).
- From 24 to 36, the difference is \(36 - 24 = 12\).
- From 36 to 54, the difference is \(54 - 36 = 18\).

The differences between the numbers are increasing by 4 each time (8, 12, 18). This suggests an **arithmetic sequence** where the differences between terms increase by a fixed amount (4 in this case).

To predict the next term:
- The difference between 54 and the next term will increase by 4 (from 18 to 22).
- Thus, the next term will be \(54 + 22 = 76\).

### Sequence: 
16, 24, 36, 54, **76**

Would you like further details on this pattern or any related concept?

Here are 5 questions that build on this:
1. What is the sum of the first 5 terms of this sequence?
2. Can you derive a formula to find the nth term of this sequence?
3. How would this sequence change if the difference between consecutive terms increased by 6 instead of 4?
4. How would the sequence behave if it were geometric instead of arithmetic?
5. What happens to the sum of the terms as you add more to the sequence?

**Tip:** Arithmetic sequences can often be represented by a simple formula: \( a_n = a_1 + (n-1) \cdot d \), where \(a_1\) is the first term and \(d\) is the common difference.

Discover how to analyze the arithmetic sequence 16, 24, 36, 54 and predict the next term. Learn about increasing differences between terms and how to apply the arithmetic sequence formula to solve problems. Suitable for students in Grades 6-8.

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