Question

Resolva a equação 2+5+8+...+×=126

Answer 1

2 + 5 + 8 + ....... + x = 126 

an = a1 + (n-1)*

x = 2 + (n-1)*3

x = 2 + 3n - 3

x = 3n - 1 . (I)

126 = (2 + 3n-1)*n/2

126 =(3n+1)*n/2

2*126 = (3n + 1)*n

252 = 3n² + n

3n² + n - 252 = 0

raízes:

n' = - 28/3

n'' = 9

n = 9

x = 3n - 1

x = 3*9 - 1

x = 27 - 1

x = 26

formula:

Sn = (a1 + an)*n/2

Sn = (2 + 26)*9/2

Sn = (28)*9/2

Sn = 28*9/2

Sn = 252/2

Sn = 126