Question

Calcule a soma dos trinta primeiros da PA (3,8,13,28)

Answer 1

$\Large\boxed{\begin{array}{l}\sf (3,8,13,28)\,n\tilde ao\,\acute e\,uma\,PA\\\sf pois\,a_4-a_3\ne a_3-a_2\\\sf ou\,seja\\\sf 28-13\ne13-8\\\sf 15\ne5.\\\sf Agora\,supondo\,que\,a\,PA\,seja\\\sf (3,8,13,18,\dotsc)\,teremos:\\\sf r=8-3=5\\\sf a_{30}=a_4+26r\\\sf a_{30}=28+26\cdot5\\\sf a_{30}=28+130\\\sf a_{30}=158.\\\sf S_{30}=\dfrac{\diagdown\!\!\!\!\!\!3\!0\cdot(3+158)}{\diagdown\!\!\!2}\\\\\sf S_{30}=15\cdot161\\\sf S_{30}=2415\end{array}}$