Règles Composées

Apprendre

Des suites combinant plusieurs opérations (comme additionner puis multiplier) pour générer chaque terme.

Compound rule sequences apply more than one operation to get from one term to the next. Common combinations include 'multiply then add', 'add then multiply', or alternating between different operations. These sequences require recognizing that a single operation won't explain the pattern.

aₙ₊₁ = f(g(aₙ)), where f and g are different operations

• 2, 5, 11, 23, 47... (×2 then +1 each step)
• 1, 3, 7, 15, 31... (×2 then +1, or 2ⁿ - 1)
• 3, 7, 15, 31... (×2 + 1 each step)

Comment le reconnaître

• Simple differences or ratios don't reveal a constant
• Try combinations: (term × k) + c or (term + c) × k
• Look for patterns like 'double and add one'
• The relationship between terms may need two operations

Erreurs fréquentes

• Assuming only one operation is involved
• Not trying different operation orders
• Missing that some compound rules simplify to formulas (like 2ⁿ - 1)

Conseils de pratique

Séquences Numériques