Find wrong number in series: 3, -15, 35, 63, 99, -143

Concept: In a ‘find the wrong number’ series, each term follows a definite generating rule. Here every term is the product of two consecutive odd numbers, with the sign alternating starting from positive: Tn = (2n − 1)(2n + 1), sign = positive for odd n, negative for even n.

1. n = 1: T1 = 1 × 3 = 3, sign positive → +3 — matches the given first term (3).

2. n = 2: T2 = 3 × 5 = 15, sign negative → −15 — matches the given second term (−15).

3. n = 3: T3 = 5 × 7 = 35, sign positive → +35 — matches the given third term (35).

4. n = 4: T4 = 7 × 9 = 63, sign negative → −63 — but the given fourth term is +63, not −63.

5. n = 5: T5 = 9 × 11 = 99, sign positive → +99 — matches the given fifth term (99).

6. n = 6: T6 = 11 × 13 = 143, sign negative → −143 — matches the given sixth term (−143).

Cross-check: Every term except the fourth satisfies Tn exactly, confirming that the alternating-sign product-of-consecutive-odd-numbers rule governs this series; the fourth term is the sole term whose sign contradicts the rule.

So the wrong number in the series is 63 (it should read −63).