Question

Determine a soma dos 20 primeiros termos da PA 3,6,9

Answer 1

S20 = (a1 + a20).20/2
S20 = [a1 + (a1 + 19r)].10
S20 = [3 + (3 + 19.3)].10
S20 = [3 + (60)].10
S20 = 630

Answer 2

Dada a P.A:

$\mathsf{\left(3,\:6,\:9,...\right)}$

Calculando sua razão:

$\mathsf{r=a_n-a_{n-1}}\\\mathsf{r=a_2-a_1}\\\mathsf{r=6-3}\\\mathsf{r=3}$

Calculando o valor do 20 termo:

$\mathsf{a_n=a_k+\left(n-k\right)r}\\\mathsf{a_{20}=a_1+\left(20-1\right)\cdot 3}\\\mathsf{a_{20}=3+\left(19\cdot 3\right)}\\\mathsf{a_{20}=3+57}\\\mathsf{a_{20}=60}$

Calculando a soma do 20 primeiros termos da P.A:

$\mathsf{S_n=\dfrac{\left(a_n+a_1\right)\cdot n}{2}}\\\\\\\mathsf{S_{20}=\dfrac{\left(60+3\right)\cdot 20}{2}}\\\\\\\mathsf{S_{20}=63\cdot 10}\\\\\\\boxed{\mathsf{S_{20}=630}}\: \: \checkmark$