Question

calcule a soma dos trinta primeiros termos da PA (4,10,...)

Answer 1

Temos então:

An= a1+(n-1)×r

A30= 4+(30-1)×6
A30= 4+29×6
A30= 4+174
A30= 178

Somando todos os valores:

Sn = (A1 + An) . n / 2
S30 = (4 + 178) . 30 / 2
S30 = 2730

Answer 2

$a_n = a_1+(n-1)*r\\\\ r = a_2-a_1 = 10-4 = 6\\\\ a_3_0 = 4+(30-1)*6\\\\ a_3_0 = 4+(29*6)\\\\ \boxed{a_3_0 = 178}$

$S_n = \frac{(a_1+a_n)*n}{2}\\\\ S_3_0 = \frac{(4+178)*30}{2}\\\\ S_3_0 = (182)*15\\\\ \boxed{S_n = 2730}$