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3.10. Logística final

Sucesiones y logística

Monigote con cascosAntes de dar por concluida la planificación financiera y logística, comprueba si dominas las herramientas necesarias para que el festival sea un éxito.

Elige una de estas opciones para repasar.

Si lo necesitas, en el desplegable hay una tabla con las claves de sucesiones.

Claves de las sucesiones

Conceptos importantes de las sucesiones
ARITMÉTICAS GEOMÉTRICAS
DEFINICIÓN

Secuencia donde la diferencia entre 2 términos consecutivos es constante. 

Secuencia donde la razón de cada término con su término anterior es constante.
FÓRMULA RECURRENTE an = an-1 + d an = r · an-1
FÓRMULA GENERAL an = a1 + (n-1) · d an = a1 · rn-1 
SUMA de n TÉRMINOS y SUMA INFINITA Sn = n (a1 + an) /2

Sn = a1 · (rn - 1) / (r - 1)

S∞ = a1 / (1 - r)
RECUERDA SUMA o RESTA para conseguir el siguiente término. MULTIPLICA o DIVIDE para conseguir el siguiente término.

Opción A: Sucesiones en el escenario

Como responsable de la organización del festival, resuelve estas situaciones, teniendo en cuenta que se empieza siempre en n = 1.

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AltavozPara cubrir el sonido de todo el recinto, el personal técnico cuelga altavoces en vertical.

Si en la primera fila de la estructura hay {a} altavoces y en cada nivel inferior se añaden siempre {d} altavoces más, calcula el número de altavoces a{n} que habrá exactamente en la fila número {n}.

Icono de electricidad en forma de rayoEl equipo de sonido aumenta el consumo eléctrico de forma constante según la potencia de salida.

Si el consumo base con el volumen al mínimo es de {a} vatios y por cada punto que subimos el regulador el consumo aumenta en {d} vatios, calcula el consumo total a{n} cuando el regulador esté en la posición {n}.

CablePara conectar los focos de la pasarela, los electricistas usan cables de diferentes longitudes.

El primer cable mide {a} metros y cada cable siguiente es exactamente {d} metros más largo que el anterior para llegar más lejos en el escenario. Calcula la longitud del cable a{n} que ocupa la posición {n} en el mazo de conexiones.

Su navegador no es compatible con esta herramienta.

Opción B: Sucesiones en el escenario

Como responsable de la organización del festival, resuelve estas situaciones, teniendo en cuenta que se empieza siempre en n = 1.

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Mano con una rueda con los signos menos y másPara que el sonido llegue al fondo del estadio, cada etapa de potencia duplica la fuerza de la señal anterior.

Si el primer amplificador emite una potencia de {a} vatios y la razón de crecimiento es {r}, calcula la potencia a{n} que alcanzará el amplificador número {n}.

Escenario con focos y altavocesLa estructura del escenario principal es modular.

La primera fila de soportes tiene {a} piezas y, por cada nivel de altura que subís, el número de piezas necesarias se multiplica por {r} para garantizar la estabilidad.

Calcula el número de piezas que tendréis que colocar en el nivel número {n}.

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Opción C: Sucesiones en el escenario

Como responsables de la oficina técnica del concierto, habéis registrado los siguientes datos sobre el material y el consumo eléctrico. Sin embargo, algunos valores se han borrado del informe.

Observad el patrón de cada sucesión y completad los huecos:

a) Número de proyectores led por cada barra de sonido:

2, 5, , 11, 14, ...

b) Incremento de la potencia en vatios según el volumen de los amplificadores:

4, 8, 24, , 480, ...

c) Metros cuadrados de superficie iluminada según la altura de la torre:

1, 4, 9, , 25, ...

d) Estado del equipo de "destellos" que da las luces de flash (3 significa encendido con flash y -3 apagado en espera):

-3, 3, -3, , -3, ...

e) Número total de personas necesarias sumando los dos equipos anteriores (sucesión tipo Fibonacci):

1, 3, 4, 7, 11, , ...

f) Sección del cableado en pulgadas para evitar el sobrecalentamiento:

1/3, 1/6, 1/9, , ...

Reflexión para el equipo de producción:

¿Cuál de estas sucesiones crece de forma más rápida? ¿Aparece alguna de ellas directamente en las diagonales del triángulo de Tartaglia?

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