Resposta :
Primeiro, calculamos a razão:
[tex]r=7-3=4[/tex]
Agora, calcularemos o 25º termo:
[tex]a_n=a_1+(n-1)r\\\\ a_{25}=3+(25-1)4\\\\ a_{25}=3+24\cdot4\\\\ a_{25}=3+96\\\\ a_{25}=99[/tex]
Agora podemos calcular a soma dos termos:
[tex]S_n=\dfrac{(a_1+a_n)n}{2}\\\\ S_{25}=\dfrac{(3+99)25}{2}\\\\ S_{25}=\dfrac{102\cdot25}{2}\\\\ S_{25}=51\cdot25\\\\ \boxed{S_{25}=1275}[/tex]
[tex]r=7-3=4[/tex]
Agora, calcularemos o 25º termo:
[tex]a_n=a_1+(n-1)r\\\\ a_{25}=3+(25-1)4\\\\ a_{25}=3+24\cdot4\\\\ a_{25}=3+96\\\\ a_{25}=99[/tex]
Agora podemos calcular a soma dos termos:
[tex]S_n=\dfrac{(a_1+a_n)n}{2}\\\\ S_{25}=\dfrac{(3+99)25}{2}\\\\ S_{25}=\dfrac{102\cdot25}{2}\\\\ S_{25}=51\cdot25\\\\ \boxed{S_{25}=1275}[/tex]