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Helga [31]
3 years ago
9

Ana escribe conjuntos de cinco enteros positivos consecutivos con la siguiente propiedad: La suma de tres de los números es tan

grande como la suma de los otros dos. ¿Cuántos conjuntos con esta propiedad ha escrito Ana?
Seleccione una:

a. 1

b. 2

c. 0

d. 3

e. Mas de 3
Mathematics
1 answer:
Keith_Richards [23]3 years ago
5 0

Answer:

a) 1.

Step-by-step explanation:

Supongamos que el primer número entero positivo es a tal que a ∈ Z⁺.

Luego, el conjunto de los cinco enteros positivos se puede expresar como

A = {a; a+1; a+2; a+3; a+4}

Dada la condición del problema, se debe cumplir que

a + (a+1) + (a+2) = (a+3) + (a+4)

⇒  3a + 3 = 2a + 7

Resolviendo la ecuación resulta

a = 4

Luego, el conjunto A nos resulta

A = {4; 5; 6; 7; 8}

Puede concluirse que sólo un conjunto cumple con esta condición.

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