Question

qual o valor da razao da progressao geometrica (x-4, x, x+20)

Answer 1

Olá Normadiana.


A razão de uma P.G é obtida pela razão de um termo pelo seu antecessor.

$\mathsf{a_1=x-4}\\\mathsf{a_2=x}\\\mathsf{a_3=x+20}\\\\\\\mathsf{q=\dfrac{x}{x-4}}~(i)\\\\\\\\\mathsf{q=\dfrac{x+20}{x}}~(ii)\\\\\\\\\mathsf{\dfrac{x}{x-4}=\dfrac{x+20}{x}}~~\gets (i)=(ii)\\\\\\\mathsf{x^2=(x+2)\cdot(x-4)}\\\\\mathsf{\diagup\!\!\!x^2=\diagup\!\!\!x^2-4x+2x-8}\\\\\mathsf{0=-2x-8}\\\\\mathsf{2x=-8}\\\\\mathsf{x=\dfrac{-8}{2}}\\\\\mathsf{x=-4}$

Calculando a razão.

$\mathsf{q=\dfrac{x}{x-4}}\\\\\\\mathsf{q=\dfrac{-4}{-4-4}}\\\\\\\mathsf{q=\dfrac{-4}{-8}}\\\\\\\boxed{\mathsf{q=\dfrac{1}{2}}}$


Dúvidas? comente.