Question

Calcule a soma dos 25 primeiros termos da p.a 3,7,11,15

Answer 1

1° vamos calcular o último termo dessa PA:

$PA(3,7,11,15, ...)\\\\ a_n=?\\ a_1=3\\ n=25\\ r=7-3\to 4\\\\ a_n=a_1+(n-1)*r\\\\ a_{25}=3+(25-1)*4\to \\ a_{25}=3+(25-1)*4\to \\ a_{25}=3+24*4\to \\ a_{25}=3+96\to \\ a_{25}=99\\\\ PA((3,7,11,15, 19, 23, 27, 31, 35, 39, 43, 47, 51,55, 59, 63, 67, 71, 75, 79,\\83,87, 91, 95, 99)$


Calculando a soma:

$S_n= \frac{(a_1+a_n)*n}{2} \\\\S_n= \frac{(3+99)*25}{2} \to \\ \\ S_n= \frac{102*25}{2} \to \\ \\ S_n= \frac{2550}{2} \to \\ \\ S_n=1275$

Answer 2

Resposta

PA: ( 3, 7....)