Question

Determine x, de modo que a sequência (4,4x,10x+6) seja pg

Answer 1

Para que seja PG a razão deve ser mantida constante em toda sequencia, logo:

$razao=\frac{a_3}{a_2}=\frac{a_2}{a_1}\\\\\frac{a_3}{a_2}=\frac{a_2}{a_1}\\\\\frac{10x+6}{4x}=\frac{4x}{4}\\\\4.(10x+6)=4x\;.\;4x\\\\40x+24=16x^2\\\\2x^2-5x-3=0\\\\\Delta=(-5)^2-4.2.(-3)\\\Delta=25+24\\\Delta=49\\\\x_1=\frac{5+\sqrt{49}}{2.2}=\frac{5+7}{4}=3\\\\x_2=\frac{5-\sqrt{49}}{2.2}=\frac{5-7}{4}=-\frac{1}{2}$