Series Completion: 4, 10, (?), 82, 244, 730

Concept: Many series-completion reasoning problems relate consecutive terms through a fixed linear recurrence of the form (previous term x k) - c, rather than a plain arithmetic (constant-difference) or geometric (constant-ratio) progression. To uncover such a rule, test whether multiplying each term by a trial constant and then adding or subtracting a fixed number reproduces the next term consistently across ALL the given terms.

Application: Test the rule against the given consecutive terms in order:

1. 4 x 3 - 2 = 10, matching the second given term.

2. Assuming the same rule generates the missing third term: 10 x 3 - 2 = 28.

3. 28 x 3 - 2 = 82, matching the fourth given term.

4. 82 x 3 - 2 = 244, matching the fifth given term.

5. 244 x 3 - 2 = 730, matching the sixth given term.

Since the same rule (multiply by 3, then subtract 2) reproduces every given term after the blank, the missing term is 28.

Cross-check: Working backward from 730 confirms it: (730+2)/3 = 244, (244+2)/3 = 82, (82+2)/3 = 28 - matching the value found above; continuing back, (28+2)/3 = 10 and (10+2)/3 = 4, matching the first given term. The rule holds consistently in both directions.