Question

calcule a soma dos 20 primeiros termos dessa pa (5,8,11,14,17...)

Answer 1

r = 8 - 5 => 3

an = a1 + (n - 1).r
an = 5 + (20 - 1).3
an = 5 + 19.3
an = 5 + 57
an = 62

Sn = (a1 + an).n / 2
S20 = (5 + 62).20 / 2
S20 = (5 + 62).10
S20 = (5 + 62).10
S20 = 67.10
S20 = 670

Answer 2

Olá, boa noite ☺

Resolução:

♦Primeiramente precisamos determinar o 20º termo dessa P.A.

$\\ \text{A}_{\text{n}}=\text{a}_{\text{1}} + ( \text{n - 1} )\cdot \text{r} \\ \\ \text{A}_{\text{20}}=\text{5} + ( \text{20 - 1} )\cdot \text{3} \\ \\ \text{A}_{\text{20}}=\text{5} + ( \text{19} )\cdot \text{3} \\ \\ \text{A}_{\text{20}}=\text{5} + \text{57} \\ \\ \text{A}_{\text{20}}=62$

O vigésimo termo é 62.

$\\ S_{20}= \dfrac{(a_{n}+a_{1})\cdot n}{2} \\ \\S_{20}= \dfrac{(62+5)\cdot 20}{2} \\ \\ S_{20}= \dfrac{67\cdot 20}{2} \\ \\ S_{20}= \dfrac{1340}{2} \\ \\ \boxed {\boxed{\bold{S_{20}= 670}}}$

Bons estudos :)