Terms: We're given the first three terms of an Arithmetic Progression:

Term 1 (a?): x - 2

Term 2 (a?): x + 2

Term 3 (a?): 2x - 1

Common Difference: Since it's an AP, the difference between consecutive terms must be the same:

a? - a? = a? - a?

Substitute the terms: Now, let's substitute the given terms into the equation:

(x + 2) - (x - 2) = (2x - 1) - (x + 2)

Solving for x:

Simplify the left side:

x + 2 - x + 2 = 4

Simplify the right side:

2x - 1 - x - 2 = x - 3

Set the simplified sides equal:

4 = x - 3

Solve for x:

add 3 to both sides of the equation.

4+3 = x-3+3

7 = x

x = 7

Therefore, the value of x is 7.