Correct Answer - Option 3 : x ∈ {-2, 4}
Concept:
Let us consider sequence a1, a2, a3 …. an is an A.P.
Common difference “d”= a2 – a1 = a3 – a2 = …. = an – an-1
Calculation:
Since x2, x, -8 are in A.P we can write,
x - x2 = - 8 - x
⇒ x2 - 2x - 8 = 0
⇒ x2 - 4x + 2x - 8 = 0
⇒ x(x - 4) + 2(x - 4) = 0
⇒ (x - 4)(x + 2) = 0
⇒ x = -2, 4
∴ x ∈ {-2, 4}