Difficulty: Medium
Correct Answer: 28
Explanation:
Introduction / Context:This sequence employs a cycle of operations rather than a single arithmetic progression. Many test series use a pattern like “small increase, big transform, correction, then repeat.” We must uncover and continue that cycle to determine the missing value.
Given Data / Assumptions:
Concept / Approach:
Look for a repeating block of operations beginning from the start: a modest increase, a strong growth jump, a correction (drop), and a recovery. Derive a minimal set of operations that exactly hit the supplied terms.
Step-by-Step Solution:
4 → 7: +3 (small grow step).7 → 25: +18 (strong jump, which can be viewed as 73 + 4).25 → 10: −15 (correction).10 → __: apply a recovery jump mirroring the earlier strong jump but scaled: 102 + 8 = 28.28 → 20: −8 (smaller correction than −15, continuing a soft-landing theme).20 → 16: −4 (further tapering correction).16 → 19: +3 (back to the small grow step that started the cycle).Verification / Alternative check:
The consistent narrative is “+3, big jump, correction, medium jump, decreasing corrections, back to +3.” Only 28 at the blank preserves all subsequent given terms without contradiction.
Why Other Options Are Wrong:
13 or 15 break the downstream transitions to 20 and 16. 20 at the blank would duplicate a later value and disrupt the measured decline to 16. 28 alone keeps every neighbor consistent.
Common Pitfalls:
Forcing a single arithmetic or geometric rule. Some sequences intentionally mix operations; the correct test is whether one choice keeps all later steps valid.
Final Answer:
28
Discussion & Comments