Question

calcule a soma dos 30 primeiros termos da p.a (52; 48; 44; ...)

Answer 1

1° vamos calcular o último termo dessa PA:

$PA(52, 48, 44, ...)\\\\\\\\ a_{30}=?\\a_1=52\\n=30\\ r=-4\\\\ a_n=a_1+(n-1)*r\\\\ a_{30}=52+(30-1)*(-4)\to \\ a_{30}=52+29*(-4)\to \\ a_{30}=52-116\to \\ a_{30}=-64$



$S_n= \frac{(a_1+a_n)*n}{2} \\\\S_{30}= \frac{(52+(-64))*30}{2} \to \\\\ S_{30}= \frac{(52-64)*30}{2} \to \\\\ S_{30}= \frac{-12*30}{2} \to \\\\ S_{30}= \frac{360}{2} \to \\\\ S_{30}=-180$