Respuesta:
la figura 8
Explicación paso a paso:
es correcto
La figura 7
La sucesión 3, 6, 10, 15, 21... responde a la ecuación:
an = (n + 1) (n+2)/2
a1 = (1 + 1) (1 + 2)/2 = (2 x 3)/2 = 6/2 = 3
a2 = (2 + 1) (2 + 2)/2 = (3 x 4)/2 = 12/2 = 6
a3 = (3 + 1) (3 + 2)/2 = (4 x 5)/2 = 20/2 = 10
a4 = (4 + 1) (4 + 2)/2 = (5 x 6)/2 = 30/2 = 15
...
La figura 10:
a10 = (10 + 1) (10 + 2) = (11 x 12)/2 = 132/2 = 66
La figura con 36 hexágonos:
(n + 1) (n + 2)/2 = 36
(n + 1) (n + 2) = 36 x 2
(n + 1) (n + 2) = 72
n² + 3n + 2 = 72
n² + 3n + 2 - 72 = 0
n² + 3n - 70 = 0
(n + 10) (n - 7) = 0
n1 = -10 se descarta por ser negativo
n2 = 7
La figura con 36 hexágonos es la 7:
n7 = (7 + 1) (7 + 2)/2 = (8 x 9)/2 = 72/2 = 36
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Respuesta:
la figura 8
Explicación paso a paso:
es correcto
Verified answer
Respuesta:
La figura 7
Explicación paso a paso:
La sucesión 3, 6, 10, 15, 21... responde a la ecuación:
an = (n + 1) (n+2)/2
a1 = (1 + 1) (1 + 2)/2 = (2 x 3)/2 = 6/2 = 3
a2 = (2 + 1) (2 + 2)/2 = (3 x 4)/2 = 12/2 = 6
a3 = (3 + 1) (3 + 2)/2 = (4 x 5)/2 = 20/2 = 10
a4 = (4 + 1) (4 + 2)/2 = (5 x 6)/2 = 30/2 = 15
...
La figura 10:
a10 = (10 + 1) (10 + 2) = (11 x 12)/2 = 132/2 = 66
La figura con 36 hexágonos:
(n + 1) (n + 2)/2 = 36
(n + 1) (n + 2) = 36 x 2
(n + 1) (n + 2) = 72
n² + 3n + 2 = 72
n² + 3n + 2 - 72 = 0
n² + 3n - 70 = 0
(n + 10) (n - 7) = 0
n1 = -10 se descarta por ser negativo
n2 = 7
La figura con 36 hexágonos es la 7:
n7 = (7 + 1) (7 + 2)/2 = (8 x 9)/2 = 72/2 = 36