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.