Step-by-step Solution:

Quick Solution

This is a classic alternating series puzzle. The sequence is actually two independent series that are interleaved.

1. Separate the Two Series

To see the pattern, let's split the main series by taking the numbers at odd and even positions:

• Series 1 (Odd positions): 3, 6, 9, ... , 12
• Series 2 (Even positions): 6, 12, __, ... , 12

The missing number is the third term in Series 2.

2. Identify the Pattern

There is a clear relationship between the two series. Each term in Series 2 is exactly double the corresponding term in Series 1.

• 1st term of Series 2 (6) = 2 × 1st term of Series 1 (3)
• 2nd term of Series 2 (12) = 2 × 2nd term of Series 1 (6)

Following this rule, the 3rd term of Series 2 must be double the 3rd term of Series 1.

3. Find the Missing Number

- The 3rd term in Series 1 is 9.
- Therefore, the missing number (the 3rd term in Series 2) is:

2 × 9 = 18

The full series would be: 3, 6, 6, 12, 9, 18, 12, 12.

Final Answer: The missing number in the given series is 18.