Find wrong number in series: 3, 15, -35, 63, -99

Concept: This series applies two independent rules at once — a MAGNITUDE rule (how large each term is) and a SIGN rule (how the sign alternates). To find the wrong number, check both rules for every term; the term that fails either check is the anomaly.

Application:

1. Magnitude check: the five terms are products of consecutive odd-number pairs — 1×3, 3×5, 5×7, 7×9, 9×11 — giving 3, 15, 35, 63, 99. These match the given magnitudes (3, 15, 35, 63, 99) exactly, so the magnitude rule holds for all five terms.

2. Sign check: from the 2nd term onward the series reads +15, -35, +63, -99 — a clean alternation, positive at even positions and negative at odd positions.

3. Extending that alternation back to the 1st term, its sign should also follow the odd-position rule, i.e. it should be negative (-3) to stay consistent with the rest of the series.

4. The series as given shows the 1st term as +3 (positive) — this contradicts the sign rule established by every other term.

Cross-check: Checking sign against position parity independently confirms it: odd positions (1st, 3rd, 5th) should be negative and even positions (2nd, 4th) positive. The 3rd term (-35) and 5th term (-99) are correctly negative, and the 2nd (15) and 4th (63) are correctly positive — only the 1st term breaks the rule, appearing as +3 instead of -3.

Answer: 3 is the wrong number in the series; it should be -3.