Let x+3, 2x+1, and 5x+2 be consecutive terms of an arithmetic sequence. find the absolute value of the common difference of the terms.

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.