Question

Descubra o valor de x na pa (x+3,2x+2,4x+8)

Answer 1

Termo geral de uma P.A:
$a_{n}=a_{1}+(n-1).r$.
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$a_{1}=x+3$
$a_{2}=2x+2$
$a_{3}=4x+8$
$r=?$
$x=?$
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n=2:
$2x+2=x+3+(2-1).r$ =>
$2x+2=x+3+r$ =>
$2x-x-r=3-2$ =>
$x-r=1$.

n=3:
$4x+8=x+3+(3-1).r$ =>
$4x+8=x+3+2r$ =>
$4x-x-2r=3-8$ =>
$3x-2r=-5$.

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$\left \{ {{x-r=1} \atop {3x-2r=-5}} \right.$ =>
$\left \{ {{(x-r=1)}.-2 \atop {3x-2r=-5}} \right.$ =>

$\left \{ {{-2x+2r=-2} \atop {3x-2r=-5}} \right.$ =>
$x=-7$.
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$3.(-7)-2r=-5$ =>
$-21-2r=-5$ =>
$2r=-21+5$ =>
$2r=-16$ =>
$r=\frac{-16}{2}$ =>
$r=-8$.

O valor de x é -7!