This sequence appears to follow a pattern involving multiplication and division. To find the next terms, let’s identify the rule governing the sequence:

Given sequence: \( 8, 24, 12, 36, 18, \ldots \)

1. From \( 8 \) to \( 24 \): Multiply by 3.  
   \( 8 \times 3 = 24 \)

2. From \( 24 \) to \( 12 \): Divide by 2.  
   \( 24 \div 2 = 12 \)

3. From \( 12 \) to \( 36 \): Multiply by 3.  
   \( 12 \times 3 = 36 \)

4. From \( 36 \) to \( 18 \): Divide by 2.  
   \( 36 \div 2 = 18 \)

The pattern is: Multiply by 3, then divide by 2, and repeat.

**Continuing the sequence:**

5. From \( 18 \), multiply by 3:  
   \( 18 \times 3 = 54 \)

6. Then, divide by 2:  
   \( 54 \div 2 = 27 \)

So, the next two numbers in the sequence are:

**54, 27**

Would you like a more detailed explanation or have any questions? Here are some related questions:

1. What are arithmetic and geometric sequences?
2. How do you find the rule of a sequence?
3. Can sequences have more than one pattern?
4. What is the significance of alternating operations in sequences?
5. How can sequences be represented graphically?

**Tip:** Always look for consistent operations in sequences like multiplication, division, addition, or subtraction to identify patterns.

Explore the patterns in arithmetic and geometric sequences with detailed examples and solutions. Learn how to identify and continue sequences using multiplication, division, addition, and subtraction operations. Suitable for students in Grades 7-9.

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