Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in A.P.

Since, (5x + 2), (4x - 1) and (x + 2) are in A.P.

Hence, difference between consecutive terms are equal.

∴ (4x - 1) - (5x + 2) = (x + 2) - (4x - 1)

⇒ 4x - 1 - 5x - 2 = x + 2 - 4x + 1

⇒ -3 - x = 3 - 3x

⇒ -3 - 3 = -3x + x

⇒ -6 = -2x

⇒ x = $\dfrac{-6}{-2}$

⇒ x = 3.

Hence, the value of x = 3.