Multiple choice

In each of the following number series only one number is wrong. Find out that wrong number. $12 \quad 11 \quad 19 \quad 45 \quad 164 \quad 795$

  1. 12

  2. 11

  3. 19

  4. 164

  5. 795

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Series: 12, 11, 19, 45, 164, 795. Pattern: 12×1-1=11, 11×2-3=19, 19×3-12=45, 45×4-16=164, 164×5-25=795. Subtractions: 1, 3, 12, 16, 25 = 1², (3), (12 not square), 4², 5². The third subtraction should be 9 (3²) not 12. If subtraction was 9: 19×3-9=48, not 45. So 19 breaks pattern. Alternative: 12-1=11, 11+8=19, 19+26=45, 45+119=164... differences follow pattern. But better: Differences are 1, 8, 26, 119, 631. These multiply by ~3. The issue is 19 - it should make the pattern 12×1-1, then ×2-2, ×3-3, ×4-4, ×5-5. Checking: 12×1-1=11, 11×2-2=20 (not 19), 20×3-3=57 (not 45). Actually 19 is wrong because it breaks ×n-1 pattern: 12×1-1=11, 11×2-1=21 (not 19).