Question

Sabe-se que a sequência (9,y,144,x) é uma PG. Determine os valores de y e x.

Answer 1

$\mathsf{a_{3}=a_{1}.{q}^{3}}\\\mathsf{144=9.{q}^{3}}\\\mathsf{q^{3}=\dfrac{144}{9}}\\\mathsf{q^{3}=16}$

$\mathsf{q=\sqrt[3]{16}=2\sqrt[3]{2}}$

$\boxed{\boxed{\boxed{\mathsf{y=9.2\sqrt[3]{2}=18\sqrt[3]{2}}}}}$

$\mathsf{x=144.2\sqrt[3]{2}}$

$\boxed{\boxed{\boxed{\mathsf{x=288\sqrt[3]{2}}}}}$