Question

Determinar a P.G. de três termos, sabendo que o produto desses termos é 216 e que a soma dos dois últimos é 18

Answer 1

Resposta:

Explicação passo-a-passo:

Três termos da PG

$a_1,a_1.q,a_1.q^{2}$

$a_1.a_2.a_3=216\\\\a_1.(a_1.q).(a_1.q^{2})=216\\\\a_1^{3}.q^{3}=6^{3}\\\\(a_1.q)^{3}=6^{3}\\\\a_1.q=6$

$a_2+a_3=18\\\\a_1.q+a_1.q^{2}=18\\\\a_1.q+a_1.q.q=18\\\\6+6q=18\\\\6q=18-6\\\\6q=12\\\\q=\frac{12}{6}\\\\\boxed {q=2}\\\\\\a_1.q=6\\\\a_1.2=6\\\\a_1=\frac{6}{2}\\\\\boxed {a_1=3}\\\\\\PG(3,3.2,3.2.2)\\\\\boxed{PG(3,6,12)}$