Which number would replace the question mark in the series 7, 12, 19, ?, 39?

Concept: When a number series shows differences between consecutive terms that themselves increase by a constant step (a second-order arithmetic pattern), the missing term is found by extending that difference pattern rather than repeating a single fixed gap.

1. Find the gap between the first two terms: 12 - 7 = 5.

2. Find the gap between the next two terms: 19 - 12 = 7. The gap increased by 2 compared to the previous gap.

3. Following this growing-gap pattern, the next gap should also increase by 2, giving 7 + 2 = 9.

4. Add this gap to 19: 19 + 9 = 28, so 28 is the missing number.

Cross-check: Continuing the same pattern, the gap after that should increase by 2 again, giving 9 + 2 = 11. Adding this to 28 gives 28 + 11 = 39, which matches the last given term in the series - confirming that 28 is correct.

Therefore, the missing number is 28.