Question

Determine o valor de m, de modo que os números m+1, 2m+4, 4m formem, nesta ordem, uma PG​

Answer 1

Resposta:

$m=-\frac{4}{3}$

Explicação passo a passo:

Temos:

$a_1=m+1\\\\a_2=2m+4\\\\a_3=4m$

Note que:

$\frac{a_2}{a_1}=\frac{a_3}{a_2}$

Portanto:

$\frac{2m+4}{m+1}=\frac{4m}{2m+4}\\\\(2m+4)^2=4m\cdot(m+1)\\\\4m^2+16m+16=4m^2+4m\\\\12m+16=0\\\\12m=-16\\\\m=-\frac{4}{3}$

Logo:

$a_1=m+1=-\frac{4}{3}+1=-\frac{1}{3}\\\\a_2=2m+4=2\cdot(-\frac{4}{3})+4=\frac{4}{3}\\\\a_3=4m=4\cdot(-\frac{4}{3})=-\frac{16}{3}\\\\q=-4$