Question

Find the value of x for which (5x + 2), (4x − 1) and (x + 2) are in AP.

Answer 1

Let the terms (5x +2), (4x -1) and (x +2) form an AP.

∴ (4x -1) - (5x +2) = (x +2) - (4x -1) [ ∵ Common difference remains constant]
⇒ -x - 3 = -3x + 3
⇒ 2x = 6
⇒ x = 3

Hence, when x = 3, the given terms are in AP.