Step-by-step Solution:

Quick Solution

This sequence does not follow a simple arithmetic pattern. The trick is to recognize that it is not one, but three separate series that are interleaved together.

1. Separate the Three Interleaved Series

If we take every third number from the original sequence, we can untangle it into three simpler series:

• Series A (starting from the 1st term): 4, 10, 16
• Series B (starting from the 2nd term): 7, __, 19
• Series C (starting from the 3rd term): 25, 20

The missing number is the middle term of Series B.

2. Identify the Patterns

• Series A (4, 10, 16): This is a simple arithmetic progression where 6 is added to each term.
• Series C (25, 20): This is an arithmetic progression where 5 is subtracted from each term.
• Series B (7, __, 19): Since the other two are simple progressions, it is highly likely this one is as well. The middle term in such a progression is the average of its neighbors.

3. Find the Missing Number

- To find the missing middle term in Series B, we can take the average of the two known terms, 7 and 19:
(7 + 19) / 2 = 26 / 2 = 13.

- We can verify this. If the series is 7, 13, 19, the difference between terms is a constant +6 (7+6=13, and 13+6=19). This forms a consistent pattern.

Final Answer: The missing number is 13.