Question

Quantos termos tem a P.A (17;26;35;...;197)?

Answer 1

Olá.

Primeiro vamos descobrir a razão (chamaremos de r).
$\mathsf{r=a_2-a_1}\\\\\mathsf{r=26-17}\\\\\mathsf{r=9}$

$\boxed{\mathsf{a_n=a_1+(n-1)\cdot r}}\\\\\\ \mathsf{197=17+(n-1)\cdot9}\\\\ \mathsf{197=17+9n-9}\\\\ \mathsf{-9n=17-9-197}\\\\ \mathsf{-9n=17-206}\\\\ \mathsf{-9n=17-206}\\\\\mathsf{-9n=-189\cdot(-1)}\\\\ \mathsf{9n=189}\\\\ \mathsf{n=\dfrac{189}{9}}\\\\\boxed{\mathsf{n=21}}$

Essa P.A tem 21 termos.

Qualquer dúvida, deixe nos comentários.
Bons estudos.

Answer 2

Boa tarde Lola

a1 = 17
a2 = 26

razão
r = a2 - a1 
r = 26 - 17 = 9 

termo geral

an = a1 + r*(n - 1)

17 + 9*(n - 1) = 197 
9*(n - 1) = 180
n - 1 = 180/9 = 20

n = 21 termos