Step-by-step Solution:

Quick Solution

This number series puzzle can be solved by looking for a pattern in the difference between the consecutive terms. This is often called a second-order series.

1. Find the Difference Between Terms

Let's write down the series and calculate the difference between each known pair of numbers:

6    12    21    __    48
  ╰─ +6 ─╯  ╰─ +9 ─╯  ╰─ ? ─╯  ╰─ ? ─╯

2. Identify the Pattern in the Differences

- The series formed by the differences is 6, 9, ... - We can see a clear pattern here: it's a simple arithmetic progression where 3 is added to get the next difference.
- The next difference in the sequence should be 9 + 3 = 12.
- The difference after that would be 12 + 3 = 15.

3. Find the Missing Number and Verify

- To find the missing number in the original series, we add the next difference (12) to the last known term (21):

21 + 12 = 33

- We can verify this result by checking if it fits the rest of the series. The next term should be 33 plus the next difference (15):
33 + 15 = 48. This matches the last number in the series, confirming our pattern is correct.

Final Answer: The missing number is 33.