Question

1) Encontre o termo geral de cada PG. ( 1/2, 1/4,....)

Answer 1

Explicação passo-a-passo:

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Temos  a seguinte PG(1/2, 1/4, ...)

Calculando a razão:

$q=\dfrac{a_{2} }{a_{1}} \\\\\\q=\dfrac{\dfrac{1}{4} }{\dfrac{1}{2} } \\\\\\q=\dfrac{1}{4} .\dfrac{2}{1} \\\\\boxed{\boxed{q=\dfrac{1}{2}}}$

Calculando o termo geral:

$a_{n}=a_{1}.q^{n-1}\\\\a_{n} =\dfrac{1}{2} .\bigg(\dfrac{1}{2}\bigg)^{n-1}\\\\a_{n} =\bigg(\dfrac{1}{2}\bigg)^{n-1+1}}\\\\\boxed{\boxed{a_{n} =\bigg(\dfrac{1}{2}\bigg)^{n}}}$