Explicação passo-a-passo:
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Temos a seguinte PG(1/2, 1/4, ...)
Calculando a razão:
[tex]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}}}[/tex]
Calculando o termo geral:
[tex]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}}}[/tex]
