Find wrong number in series: 12, 25, 49, 99, 187, 395, 789

Concept: In a "find the wrong number" series, every term is generated from the one before it by a single consistent rule. Here the rule alternates: multiply the previous term by 2 and add 1, then multiply by 2 and subtract 1, and so on. You confirm the rule against the first few terms, then apply it across the whole series — the one term where the actual value disagrees with the rule's prediction is the wrong number.

Application:

1. 12 × 2 + 1 = 25 — matches the given term.

2. 25 × 2 − 1 = 49 — matches the given term.

3. 49 × 2 + 1 = 99 — matches the given term.

4. 99 × 2 − 1 = 197, but the series shows 187 in that position — a mismatch.

5. Continuing forward with the rule's own value, 197 (not 187): 197 × 2 + 1 = 395 — matches the given term.

6. 395 × 2 − 1 = 789 — matches the given term.

Cross-check: Substituting 197 in place of 187 makes every single term in the series fit the alternating ×2 +1/−1 rule with no further adjustment needed anywhere else. Since 187 is the only term that breaks the otherwise-consistent pattern, 187 is confirmed as the wrong number in the series.