Aprender
Secuencias que combinan múltiples operaciones (como sumar y luego multiplicar) para generar cada término.
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)
Cómo reconocerlo
- 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
Errores comunes
- Assuming only one operation is involved
- Not trying different operation orders
- Missing that some compound rules simplify to formulas (like 2ⁿ - 1)
Resolución paso a paso
Encuentra el siguiente término: 2, 5, 11, 23, 47, ?
- Prueba diferencias: 3, 6, 12, 24 - no constantes, ¡pero se duplican!
- Prueba la regla: ×2 luego +1 en cada término
- Continúa: 5×2+1=11 ✓, 11×2+1=23 ✓, 23×2+1=47 ✓
- Aplica la regla: 47×2+1 = 95
Respuesta: 95