Find the next term in the pattern: 4, 7, 12, 19, 28, ? — use first differences to maintain the sequence’s internal arithmetic consistency.

Introduction / Context:This classic “increasing differences” series often grows by consecutive odd numbers. Identifying that structure lets you extend the series cleanly.

Given Data / Assumptions:

• Terms: 4, 7, 12, 19, 28, ?
• We expect a steady progression in differences, likely simple odd increments.

Concept / Approach:Compute first differences. If they form a recognizable arithmetic sequence, apply the next difference to obtain the next term.

Step-by-Step Solution:

Verification / Alternative check:All gaps are odd and increase by 2 each time; continuing with +11 yields a coherent continuation.

Why Other Options Are Wrong:

• 30 or 36 would require smaller differences (2 or 8) that break the odd-number progression.
• 49 would need a jump of +21, skipping the +11 step entirely.

Common Pitfalls:Assuming multiplicative patterns too early. With short series, first differences provide the most reliable initial test.

Final Answer:39