The numbers you've listed (16, 24, 36, 54) seem to form a sequence. Let's analyze it.

### Step 1: Find the pattern (if it's an arithmetic or geometric sequence):
To check if it's an **arithmetic sequence**, calculate the differences between consecutive numbers:
- \( 24 - 16 = 8 \)
- \( 36 - 24 = 12 \)
- \( 54 - 36 = 18 \)

The differences are not constant, so this is not an arithmetic sequence.

### Step 2: Analyze the ratio (if it's a geometric sequence):
To check if it's a **geometric sequence**, calculate the ratios between consecutive numbers:
- \( \frac{24}{16} = 1.5 \)
- \( \frac{36}{24} = 1.5 \)
- \( \frac{54}{36} = 1.5 \)

Since the ratio is constant (\( 1.5 \)), this forms a geometric sequence.

### Step 3: General formula of a geometric sequence:
A geometric sequence follows the formula:
\[
a_n = a_1 \cdot r^{n-1}
\]
Where:
- \( a_1 = 16 \) (first term)
- \( r = 1.5 \) (common ratio)

Thus, the sequence is \( 16, 24, 36, 54, \dots \), and you can find the next terms by multiplying by 1.5.

Would you like to know more details or have any questions?

Here are 5 related questions:
1. What is the next number in this geometric sequence?
2. How do you find the sum of the first \( n \) terms of a geometric sequence?
3. Can you derive the general term formula for this sequence?
4. What is the common difference in an arithmetic sequence, and how does it compare to a geometric sequence?
5. What is the importance of geometric sequences in real-world applications?

**Tip:** In geometric sequences, the ratio between terms remains constant, while in arithmetic sequences, the difference between terms is constant.

Explore the geometric sequence 16, 24, 36, 54 with a common ratio of 1.5. This step-by-step solution helps students in Grades 7-9 understand how to identify and calculate the next terms of the sequence using the geometric formula.

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