Question

If (5x + 2), (4x − 1) and (x + 2) are in AP, then x = ?

Answer 1

Let (5x + 2), (4x − 1) and (x + 2) are consecutive terms of an AP.
Then we have:
(4x − 1) − ​(5x + 2) = ​(x + 2) − ​(4x − 1)
⇒ (−x − 3) = (−3x + 3)
⇒ 2x = 6
⇒ x = 3
∴ If (5x + 2), (4x − 1) and (x + 2) are in AP, then x = 3.