Méthode des Différences

Apprendre

Une technique systématique pour identifier des motifs en calculant les différences entre termes consécutifs.

The difference method is a fundamental problem-solving technique for number sequences. By calculating the differences between consecutive terms, you can often reveal the underlying pattern. If the first differences are constant, it's arithmetic. If the first differences vary but the second differences are constant, it's quadratic. This method systematically uncovers hidden structure in sequences.

First differences: dₙ = aₙ₊₁ - aₙ

• Sequence: 2, 5, 8, 11 → Differences: 3, 3, 3 (constant = arithmetic)
• Sequence: 1, 4, 9, 16 → Differences: 3, 5, 7 → Second differences: 2, 2 (quadratic)
• Sequence: 2, 6, 18, 54 → Differences: 4, 12, 36 (not constant, try ratios instead)

Comment le reconnaître

• Write out the differences between consecutive terms
• If differences are constant, you found the pattern
• If not constant, calculate differences of differences (second differences)
• Continue until you find a constant level

Erreurs fréquentes

• Stopping too early - sometimes you need second or third differences
• Using differences on geometric sequences (use ratios instead)
• Arithmetic errors in subtraction

Conseils de pratique

Séquences Numériques