Find wrong number in series: -2, 4, 6, 8, -10

Concept: In a “find the wrong term” number series, first find a single formula Tn (the nth term as a function of its position n) that fits nearly every given term; the one term that breaks this rule is the wrong number.

Application:

1. The magnitudes of the terms are 2, 4, 6, 8, 10 — each is 2 times its position n, so the magnitude rule is 2n.

2. The sign must flip with position under the alternating factor (-1)n — negative at odd positions (1st, 3rd, 5th) and positive at even positions (2nd, 4th); combined with the magnitude rule 2n, the full governing rule is Tn = (-1)n × 2n.

3. T1 = (-1)1 × 2(1) = -2, which matches the given first term.

4. T2 = (-1)2 × 2(2) = 4, which matches the given second term.

5. T3 = (-1)3 × 2(3) = -6, but the series gives the third term as 6 — this is a mismatch.

6. T4 = (-1)4 × 2(4) = 8, which matches the given fourth term.

7. T5 = (-1)5 × 2(5) = -10, which matches the given fifth term.

Cross-check: Looking at the sequence independently of sign, the magnitudes 2, 4, 6, 8, 10 form a clean arithmetic run of multiples of 2, and the sign should be negative at the first, third and fifth positions and positive at the second and fourth positions. At the third position the sign shown is positive when it should be negative — this independently confirms the same deviation found above.

So the term shown as 6 breaks the pattern; the rule predicts -6 in its place, making 6 the wrong number in the series.