Put n = 1

A₁= -4(1)² + 15 = 11

Put n = 2

A₂= -4(2)² + 15 = -1

Put n = 3

A₃= -4(3)² + 15 = -21

Common difference, d₁= a₂ – a₁ = -1 – 11 = -12

Common difference, d₂= a₃ – a₂ = -21 + 1 = 20

Since, d₁ ≠ d₂

Therefore, it’s not an A.P.