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

2023

Find wrong number in series:

2, 3, 6, 0, 8, -3, 14, -6

  1. A.

    3

  2. B.

    0

  3. C.

    8

  4. D.

    -3

Attempted by 1 students.

Show answer & explanation

Correct answer: C

In an alternating (interwoven) number series, the terms split into two independent subsequences by position — all odd-positioned terms form one sequence and all even-positioned terms form another — and each subsequence follows its own constant arithmetic rule (here, a fixed addition or subtraction). The wrong number is the single term that breaks its own subsequence's rule while every other term, in both subsequences, fits perfectly.

Applying this to the given series:

  1. Split the series by position: odd-position terms (1st, 3rd, 5th, 7th) = 2, 6, 8, 14; even-position terms (2nd, 4th, 6th, 8th) = 3, 0, -3, -6.

  2. Check the even-position subsequence: 3 - 3 = 0, 0 - 3 = -3, -3 - 3 = -6. Every step follows a constant 'subtract 3' rule with no exception.

  3. Check the odd-position subsequence: 2 + 4 = 6 holds, but the next step should be 6 + 4 = 10, whereas the series shows 8 at that position — the rule breaks here.

  4. Confirm the rule forward: if that term were 10, then 10 + 4 = 14, which matches the actual next odd-position term (14) in the series.

Cross-check: the even-position subsequence's constant '-3' rule holds across all four of its terms with no exception, and continuing the odd-position '+4' rule from 10 correctly reaches 14 — this isolates the break to a single term, confirming it is not a mis-split of the series.

Result: the number 8 breaks the pattern of its own subsequence; the correct value at that position should have been 10, so 8 is the wrong number in the series.

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