Question

calcule a soma dos doze termos da PA (3,8,13,18,...)

Answer 1

a12 = 3 + 5.12 ==> a12 = 3+60= 63
  

S12 =  ( 3 + 63).12 ==> S12 = 66.6 ==> 396
                 2

Answer 2

Vamos primeiramente determinar o termo $a_{12}$.

$a_1=3 \\ a_2=8 \\ a_3=13 \\ n =12 \\ r =8-3=5 \\ \\ a_n=a_1+(n-1)*r \\ a_n=3+(12-1)*5 \\ a_n=3 +11*5 \\ a_n=3+55 \\ a_n=58$

Soma dos termos:
$S_{12}= \frac{(a_1+a_1_2)*n}{2} \\ \\ S_{12}= \frac{(3+58)*12}{2} \\ \\ S_{12}= \frac{61*12}{2} \\ \\ S_{12}= \frac{732}{2} \\ \\ S_{12}=366$

Espero ter ajudado. Valeu!