Number series – increasing gaps (+3, +4, +5, +6, ...): 12, 15, 19, 24, ? Continue the pattern to find the next term.

Introduction / Context:Arithmetic-difference ladders where the increment grows by 1 each time are extremely common. Recognizing the ladder saves time.

Given Data / Assumptions:

• Series: 12, 15, 19, 24, ?
• Observed first differences: +3, +4, +5, +6 next.

Concept / Approach:Apply the next increment (+6) to the latest term to get the next value.

Step-by-Step Solution:

Verification / Alternative check:Extending further would continue +7, +8, … forming a smooth progression.

Why Other Options Are Wrong:

Common Pitfalls:Overcomplicating with powers; the simple ladder fits perfectly.

Final Answer:30