Uncover the Property in the Number Set: 8, 12, 18, 27

To solve this problem, we'll follow these steps:

• Step 1: Determine if there's a consistent pattern between the numbers
• Step 2: Test for arithmetic progression
• Step 3: Test for geometric progression
• Step 4: Choose the correct option based on calculations

Now let's process each step:

Step 1: Check for Arithmetic Progression

The differences between the numbers are calculated as follows:

• $12 - 8 = 4$
• $18 - 12 = 6$
• $27 - 18 = 9$

The differences are not equal ($4, 6, \text{and } 9$), so it's not an arithmetic sequence.

Step 2: Check for Geometric Progression

Calculate the ratios between consecutive numbers:

• $\frac{12}{8} = 1.5$
• $\frac{18}{12} = 1.5$
• $\frac{27}{18} = 1.5$

The ratios are the same ($1.5$), indicating a geometric progression where each number is multiplied by $1.5$.

Conclusion: The numbers $8, 12, 18, 27$ form a geometric sequence with a common ratio of $\times 1.5$.

Therefore, the property of the sequence is $\times 1.5$.