Correct Answer - Option 3 : x ∈ {-2, 4}

**Concept:**

Let us consider sequence a_{1}, a_{2}, a_{3} …. an is an A.P.

Common difference “d”= a_{2} – a_{1} = a_{3} – a_{2} = …. = a_{n} – a_{n-1}

**Calculation:**

Since x^{2}, x, -8 are in A.P we can write,

x - x^{2} = - 8 - x

⇒ x^{2} - 2x - 8 = 0

⇒ x^{2} - 4x + 2x - 8 = 0

⇒ x(x - 4) + 2(x - 4) = 0

⇒ (x - 4)(x + 2) = 0

⇒ x = -2, 4

**∴ x ∈ {-2, 4}**