Question

Un caracol decide subir un monte en 41 dias,de manera que forme una progresión aritmetica.Si el primer dia logro subir un metro ,¿Cual debe ser el incremento diario que debe hacer para cubrir los 131,2 metros que tiene el monte ?

Answer 1

Ani,
En la PA tenemos
a1 = 1                               Usamos 
a41 = ??                           Término general: an = a1 + (n - 1).d         (1)

n = 41                                Suma de términos: Sn = n/2(a1 + an)      (2)

d = ??
Sn = 131,2                        Resolviendo sistema (1) (2)
                                                   De (2)
                                                                  2.Sn = n.a1 + n.an
                                                                2Sn - n.a1 = n.an
                                                                           an = (2Sn - n.a1)/n            (3)

                                                   (3) = (1)
                                                                          (2Sn  - n.a1)/n = a1 + (n - 1).d
                                                  Reemplazando los datos que tenemos
                                                                  [2(131.2) - 41(1)]/41 = 1 + (41 - 1).d
                                                   Efectuando
                                                                 (262.4 - 41)/41 = 1 + 40.d
                                                                 (221.4)/41 - 1 = 40.d                                                                   5.4 - 1 = 40d
                                                                  (4.4)/40 = d
                                                                   d = 0.11

                        Incremento diario debe ser 0.11m    respuesta

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