Find wrong number in series: 1, -6, 18, -54, 162, -486

Concept: A number series follows a fixed rule linking each term to the one before it (here, multiplication by a constant ratio). To find the wrong number, establish that rule from the terms that are mutually consistent, then check whether the remaining term obeys the same rule — the one that does not is the anomaly.

Application:

1. Compare each pair of consecutive terms from the second term onward: -6, 18, -54, 162, -486.

2. Compute the ratio of each pair: 18 ÷ (-6) = -3, (-54) ÷ 18 = -3, 162 ÷ (-54) = -3, (-486) ÷ 162 = -3 — a consistent common ratio of -3.

3. Apply the same ratio backward to find the term that should precede -6: required term × (-3) = -6, so required term = (-6) ÷ (-3) = 2.

4. Compare this required value with the given first term: the series shows 1, but the rule demands 2.

Cross-check: Rebuilding the series from 2 using the ×(-3) rule at every step reproduces 2, -6, 18, -54, 162, -486 exactly — confirming -3 is the true ratio and that 1 is the term that violates it.

Answer: 1 is the wrong number in the series.