Question

dertemine a soma dos dezoitos primeiros termos da P.A (1 ,5 ,9 ...).?

Answer 1

Dados:

$\displaystyle \mathsf{a_1 = 1}\\ \displaystyle \mathsf{r = 4}\\ \displaystyle \mathsf{n = 18}\\ \displaystyle \mathsf{a_n = ?}\\ \displaystyle \mathsf{S_n = ?}$

Cálculo:

$\displaystyle \mathsf{a_n = a_1 + (n-1).r}\\ \displaystyle \mathsf{a_{18} = 1 + (18 - 1).4}\\ \displaystyle \mathsf{a_{18} = 1 + 17.4}\\ \displaystyle \mathsf{a_{18} = 1 + 68}\\ \displaystyle \mathsf{a_{18} = 69}$

$\displaystyle \mathsf{S_n = \frac{(a_1 + a_n).n}{2}}\\ \\ \displaystyle \mathsf{S_{18} = \frac{(1 + 69).18}{2}}\\ \\ \displaystyle \mathsf{S_{18} = 70.9}\\ \\ \displaystyle \mathsf{S_{18} = 630}$

Resposta: 630

Answer 2

Encontrar a razão da PA

r = a2 - a1
r = 5 - 1
r = 4 

===

Encontrar o valor do termo a18:



an =   a1 + ( n -1 ) . r
a18 =  1 + ( 18 -1 ) . 4
a18 =  1 + 17 . 4
a18 =  1 + 68
a18 =  69

===

Soma:

Sn = ( a1 + an ) . n /  2  
Sn = ( 1 + 69 ) . 18 /  2   
Sn = 70 . 9  
Sn = 630