Number series – fill in the missing term. Sequence: 4, 7, 25, 10, __, 20, 16, 19, …

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:

• Sequence: 4, 7, 25, 10, __, 20, 16, 19, …
• Differences and operations appear to alternate between additive and more complex steps.
• We only need one consistent rule that reproduces all given neighbors.

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:

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