Respostas

2013-09-06T18:31:44-03:00
O problema nos diz que:

n=24\hspace{2.0cm}a_1=1\hspace{2.0cm}S_{24}=3612

Utilizando a fórmula da soma dos termos da PA, temos:

n=\dfrac{(a_1+a_n)n}{2}\Longrightarrow S_{24}=\dfrac{(a_1+a_{24})24}{2}\Longrightarrow 3612=(1+a_{24})12\\\\
\Longrightarrow3612=12+12a_{24}\Longrightarrow3600=12a_{24}\Longrightarrow a_{24}=\dfrac{3600}{12}\Longrightarrow a_{24}=300

Aplicando a fórmula do termo geral podemos descobrir a razão:

a_n=a_1+(n-1)r\Longrightarrow a_{24}=a_1+(24-1)r\Longrightarrow 300=1+23r\\\\
\Longrightarrow 23r=299\Longrightarrow r=\dfrac{299}{23}\Longrightarrow\boxed{r=13}
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