Two patterns are shown.Pattern A4, 12, 36, 108, ...The pattern continues to grow in the same way.Pattern B21, 49, 77, 105, ...The pattern continues to increase by the same amount.How much greater is the term value of the 6th term in Pattern A than the 6th term in Pattern B?
Question
Two patterns are shown.Pattern A4, 12, 36, 108, ...The pattern continues to grow in the same way.Pattern B21, 49, 77, 105, ...The pattern continues to increase by the same amount.How much greater is the term value of the 6th term in Pattern A than the 6th term in Pattern B?
Solution
Primero, identifiquemos la regla de crecimiento para cada patrón.
Para el Patrón A:
- 4, 12, 36, 108, ... Observamos que cada término se obtiene multiplicando el término anterior por 3.
- 4 * 3 = 12
- 12 * 3 = 36
- 36 * 3 = 108
Entonces, la regla de crecimiento es multiplicar por 3.
Para encontrar el 6º término en el Patrón A:
- 4º término: 108
- 5º término: 108 * 3 = 324
- 6º término: 324 * 3 = 972
Para el Patrón B:
- 21, 49, 77, 105, ... Observamos que cada término se obtiene sumando 28 al término anterior.
- 21 + 28 = 49
- 49 + 28 = 77
- 77 + 28 = 105
Entonces, la regla de crecimiento es sumar 28.
Para encontrar el 6º término en el Patrón B:
- 4º término: 105
- 5º término: 105 + 28 = 133
- 6º término: 133 + 28 = 161
Finalmente, para encontrar cuánto mayor es el valor del 6º término en el Patrón A que en el Patrón B:
- 6º término en Patrón A: 972
- 6º término en Patrón B: 161
La diferencia es: 972 - 161 = 811
Por lo tanto, el valor del 6º término en el Patrón A es 811 unidades mayor que el valor del 6º término en el Patrón B.
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