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Hallar " \( x-y \) " en la sucesion: \[ 2 ; 3 ; 2 ; 4 ; 4 ; 6 ; 12 ; 9 ; x ; y \] \( \begin{array}{ll}\text { A) } 35 & \text { B) } 36 \\ \text { D) } 41 & \text { C }\end{array} \)

Ask by Hobbs Collins. in Peru
Jan 21,2025

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Tutor-Verified Answer

Answer

\( x - y = 35 \), opción A

Solution

Para resolver el problema, analicemos la sucesión dada: \[ 2 ; 3 ; 2 ; 4 ; 4 ; 6 ; 12 ; 9 ; x ; y \] Podemos observar que hay dos subsucesiones intercaladas: 1. **Posiciones impares:** 1ª, 3ª, 5ª, 7ª, 9ª - **Valores:** 2, 2, 4, 12, \( x \) - **Patrón:** - \( 2 \times 1 = 2 \) - \( 2 \times 2 = 4 \) - \( 4 \times 3 = 12 \) - Siguiendo el patrón, \( 12 \times 4 = 48 \). Por lo tanto, \( x = 48 \). 2. **Posiciones pares:** 2ª, 4ª, 6ª, 8ª, 10ª - **Valores:** 3, 4, 6, 9, \( y \) - **Patrón:** - \( 3 + 1 = 4 \) - \( 4 + 2 = 6 \) - \( 6 + 3 = 9 \) - Siguiendo el patrón, \( 9 + 4 = 13 \). Por lo tanto, \( y = 13 \). Finalmente, calculamos \( x - y \): \[ 48 - 13 = 35 \] **Respuesta correcta: A) 35**

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Bonus Knowledge

En la sucesión dada, podemos observar que hay dos patrones diferentes que se alternan. Los números en las posiciones impares son 2, 2, 4, 12 y los números en las posiciones pares son 3, 4, 6, 9. Al observar más de cerca, podemos notar que los números en posiciones impares parecen multiplicarse por 2 y luego por 3, y los números en posiciones pares aumentan en una secuencia aritmética. Siguiendo estos patrones, podemos deducir que \( x = 36 \) y \( y = 41 \). Por lo tanto, \( x - y \) sería \( 36 - 41 = -5 \).

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