PA (1 – 3x, x – 2, 2x + 1)
A propriedade da P.A nos diz que :
[tex]\displaystyle \text a_2 = \frac{\text a_1+\text a_3}{2}[/tex]
Substituindo :
[tex]\displaystyle \text x-2 = \frac{1-3\text x+2\text x +1 }{2}[/tex]
[tex]\displaystyle 2(\text x-2) = 2-\text x[/tex]
[tex]\displaystyle 2\text x-4 = 2-\text x[/tex]
[tex]3\text x = 6[/tex]
[tex]\boxed{\text x = 2}[/tex]
P.G (- 2 + y, 2 + y, y + 14)
A propriedade da P.G nos diz que :
[tex](\text a_2)^2 = \text a_1.\text a_3[/tex]
Substituindo :
[tex](2+\text y)^2 = (-2+\text y)(\text y+14 )[/tex]
[tex]4+4\text y+\text y^2 = -2\text y - 28 + \text y^2 + 14\text y[/tex]
[tex]4+4\text y = 12\text y - 28[/tex]
[tex]8\text y = 32[/tex]
[tex]\boxed{\text y = 4}[/tex]
Portanto :
[tex]\text{2x+8y} \to 2.2 +8.4 \to 4+32 =36 \\\\\huge\boxed{\text{2x+8y = 36 }}\checkmark[/tex]
