Question

calcule a soma dos 30 primeiros termos da p.a (3,6,9,12)

Answer 1

Primeiro encontrar o último termo:

$PA~(3,6,9,12,...)\\\\\\ a_1=3\\r=6-3\to 3\\n=30\\ a_{30}=?\\\\\\ a_n=a_1+(n-1)\times r\\\\\\ a_{30}=3+(30-1) \times 3\to\\\\ a_{30}=3+29 \times 3\to\\\\ a_{30}=3+87\to\\\\ \large\boxed{a_{30}=90}$



Agora calculamos a soma:

$S_n= \dfrac{(a_1 +a_n)\times n}{2} \\\\\\ S_n= \dfrac{(3+90)\times 30}{2} \to \\\\\\ S_n= \dfrac{93\times 30}{2} \to \\\\\\ S_n= \dfrac{2790}{2} \to \\\\\\ \large\boxed{\boxed{S_n=1395}}$