Question

seja a PG ( 1, x , y , 216, ... ) calcule a razão dessa PG, o valor de x e o valor de y

ME AJUDEMM PLEASE ​

Answer 1

PG ( 1, x , y , 216, ... )

O termo da geral da PG é da forma :

$\text a_\text n = \text a_1.\text q^{\text n-1}$

Temos que :

$\text a_4 = 2016 \ ; \ \text a_1= 1 \\\\ \text{Da{\'i}}: \\\\ \text a_4=\text a_1.\text q^{4-1} \\\\ 216=1.\text q^{3} \\\\ \text q=\sqrt[3]{216} \\\\ \text{Portanto a raz{\~a}o vale}: \\\\ \huge\boxed{\text q = 6\ }\checkmark$

Os valores de x e de y :

Valor de x

$\text a_2=\text 1.\text q^{2-1} \\\\ \text x=1.6^{1} \\\\ \huge\boxed{\text x=6}\checkmark$

Valor de y

$\text a_3=\text a_1.\text q^{3-1} \\\\ \text y =1.6^{2} \\\\ \huge\boxed{\text y = 36 }\checkmark$