Find the next term in the pattern: 4, 7, 12, 19, 28, ? — use first differences to maintain the sequence’s internal arithmetic consistency.
Verbal Reasoning
Series Completion
Difficulty: Easy
Choose an option
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A30
-
B36
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C39
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D49
Answer
Correct Answer: 39
Explanation
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:
Differences: 7 − 4 = 3; 12 − 7 = 5; 19 − 12 = 7; 28 − 19 = 9.The differences are 3, 5, 7, 9 — consecutive odd numbers.Next difference = 11.Next term = 28 + 11 = 39.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