Question

Qual a razao da pg (a, a+3, 5a.3, 8a).

Answer 1

$\boxed{(a_2)^2 = a_1*a_3}\\\\ (a+3)^2 = a*(5a-3)\\\\ a^2+6a+9 = 5a^2-3a\\\\ 4a^2-9a-9 = 0\\\\ \Delta = 81+144\\\\ \Delta = 225$

$a = \frac{9+\ ou\ -15}{8}\\\\ a^i = \frac{9+15}{8} = \frac{24}{8} = 6\\\\ a^i^i = \frac{9-15}{8} = \frac{-3}{4}$

$a_1 = a = 3\\\\ a_2=a+3 = 3+3 = 6\\\\ a_3 = 5a-3 = 12$

$q= \frac{a_2}{a_1}\\\\ q = \frac{6}{3}\\\\ \boxed{q=2}$