Question

) Calcule a razão da seguinte P.g( √2,3√2 9√2...) ​

Answer 1

Resposta:

Explicação passo-a-passo:

Basta dividir um termo por seu anterior

$q=\frac{3\sqrt{2}}{\sqrt{2}}\\ \\q=3$

Para determinar o 15 termo da PG(64,32,16,...)

Razão

$q=\dfrac{32}{64}=\dfrac{1}{2}$

Temos

$a_1=64\\\\q=\frac{1}{2}\\\\n=15\\\\queremos\\\\a_1_5$

Fórmula do termo geral de uma PG

$a_n=a_1.q^{n-1}\\\\substituindo\\\\a_1_5=64.(\dfrac{1}{2})^{15-1}\\\\a_1_5=64.(\dfrac{1}{2})^{14}\\\\a_1_5=64.(\dfrac{1^{14} }{2^{14}})\\\\a_1_5=2^{8} .(\dfrac{1}{2^{14}})\\\\a_1_5=\dfrac{2^{8}}{2^{14}}\\\\a_1_5=\dfrac{1}{2^{6}}\\\\a_1_5=\dfrac{1}{64}$