Question

determine a razão e o primeiro termo da PG A4 = 1/6 e a 7 = 9/2

Answer 1

$a7 = a4. {q}^{3} \\ q = \sqrt[3]{ \frac{a7}{a4} } \\ q = \sqrt[3]{ \frac{ \frac{9}{2} }{ \frac{1}{6} } }$

$q = \sqrt[3]{ \frac{9}{2}.6} \\ q = \sqrt[3]{27} \\ q =3$

$a4 = a1. {q}^{3} \\ a1 = \frac{a4}{ {q}^{3} } \\ a1 = \frac{ \frac{1}{6} }{ {3}^{3} } = \frac{ \frac{1}{6} }{27} = \frac{1}{6}. \frac{1}{27} = \frac{1}{162}$