If the numbers are in arithmetic sequence, this means that the difference between the consecutive terms is equal.
Difference between first and second terms,
D1 = (2x + 1) - (x + 3)
D1 = x - 2
Difference between second and third terms,
D2 = (5x + 2) - (2x + 1)
D2 = 3x + 1
Equating the differences,
D1 = D2
x - 2 = 3x + 1
Transposing the variables and constants to each of the sides of the equation,
x - 3x = 1 + 2
-2x = 3
Dividing the equation by -2,
x = -3/2
Substituting this value to either of the difference,
D1 = x - 2 = (-3/2) - 2 = -7/2
The absolute value of the difference is 7/2. Thus, the answer is 7/2.
