Question

Ultilizando a propriedade das progressoes geometricas calcule o valor de x na sequencia(x+1,x,x+2) e depois escreva a pg.

Answer 1

$a_1=x+1 \\ a_2=x \\ a_3=x+2 \\ \\ \frac{a_2}{a_1} = \frac{a_3}{a_2} \\ \\ \frac{x}{x+1} = \frac{x+2}{x} \\ \\ (x+1(x+2)=x.x \\ \\ x^2+2x+x+2=x^2 \\ \\ \not x^2-\not x^2+3x=-2 \\ \\ 3x=-2 \\ \\ x=- \frac{2}{3}$


vamos substituir x

$a_1=- \frac{2}{3} +1= \frac{-2+3}{3} = \frac{1}{3} \\ \\ a_2=- \frac{2}{3} \\ \\ a_3= -\frac{2}{3} +2= \frac{-2+6}{3} = \frac{4}{3} \\ \\ P.G.=( \frac{1}{3} ,- \frac{3}{4} , \frac{4}{3} )$