Question

As raízes de uma equação do 2° grau x²-5x+4=0 são o 1° e o 2° termo de uma PG crescente . Determine o 6° termo dessa PG

Answer 1

$\displaystyle \text x^2-5\text x+4=0 \\\\ \text x = \frac{-(-5)\pm\sqrt{(-5)^2-4.4}}{2.1} \to \text x = \frac{5\pm\sqrt{25-16}}{2} \\\\\\ \text x= \frac{5\pm\sqrt{9}}{2} \to \text x=\frac{5\pm3}{2} \\\\\ \text x = 2 \ ; \ \text x = 4$

Temos a PG :

(2,4, ... )

razão :

$\displaystyle \frac{\text a_2}{\text a_1} \to \frac{4}{2} = 2$

Sexto termo :

$\text a_6 = \text a_1.\text q^{5} \\\\ \text a _6 =2.2^5 \\\\ \text a_6=2^{6}\\\\ \huge\boxed{\text a_6=64 }\checkmark$