Find wrong number in series: 2, 3, 6, 0, 8, -3, 14, -6

Concept:

In a mixed (alternating) number series, split the sequence into two sub-series -- the terms at odd positions and the terms at even positions -- and find the arithmetic pattern (common difference) governing each sub-series separately. The wrong number is the one term that breaks the pattern of its own sub-series, once every other term in both sub-series fits.

Application:

1. Odd-position terms (1st, 3rd, 5th, 7th): 2, 6, 8, 14.

2. Test the pattern: 2 + 4 = 6, which holds.

3. Next expected term: 6 + 4 = 10, but the series shows 8 instead -- the pattern breaks here.

4. The next term, 14, equals 10 + 4, confirming the series resumes the +4 pattern right after the expected 10 -- so the break is isolated to this one term.

5. Even-position terms (2nd, 4th, 6th, 8th): 3, 0, -3, -6.

6. Test the pattern: 3 - 3 = 0, 0 - 3 = -3, -3 - 3 = -6 -- every term fits; this sub-series has no break.

Cross-check:

Replacing 8 with 10 makes the full series 2, 3, 6, 0, 10, -3, 14, -6 -- both sub-series (2, 6, 10, 14 rising by 4; 3, 0, -3, -6 falling by 3) are now fully consistent, confirming 8 is the unique wrong number.

Result: 8 is the wrong number in the series.