Question

Determine o valor de x para que x/2, 4x+1 e 3x/2+2 seja uma pa

Answer 1

PA [x/2, 4x + 1, 3x/2 + 2, ...]

r = [4x + 1] - x/2
r = [8x + 2 - x]/2 
r = [7x + 2]/2

r = [3x/2 + 2] - [4x + 1]
r = 3x/2 + 2 - 4x - 1
r = [3x + 2*2 - 2*4x - 2*1]/2
r = [3x + 4 - 8x - 2]/2
r = [- 5x + 2]/2

[7x + 2]/2 = [- 5x + 2]/2
7x + 2 = - 5x + 2
7x + 5x = 2 - 2
12x = 0
x = 0/12
x = 0

PA [0/2, 4*0 + 1, 3*0/2 + 2, ...]
PA [ 0, 1, 2, ...]