A.P is known for Arithmetic Progression whose common difference = a_n – a_n-1 where n > 0

a₁ = 3, a₂ = -1, a₃ = -5, a₄ = -9

Now, a₂ – a₁ = -1 – 3 = -4

a₃ – a₂ = -5 – (-1) = -5 + 1 = -4

a₄ – a₃ = -9 – (-5) = -9 + 5 = -4

As, a₂ – a₁ = a₃ – a₂ = a₄ – a₃

The given sequence is A.P

Common difference, d = a₂ – a₁ = -4

To find next three more terms of A.P, firstly find a_n

We know, a_n = a + (n-1) d where a is first term or a₁ and d is common difference

∴ a_n = 3 + (n-1) -4

⇒ a_n = 3 – 4n + 4

⇒ a_n = 7 – 4n

When n = 5:

a₅ = 7 – 4(5)

⇒ a₅ = 7 – 20

⇒ a₅ = -13

When n = 6:

a₆ = 7 – 4(6)

⇒ a₆ = 7 – 24

⇒ a₆ = -17

When n = 7:

a₇ = 7 – 4(7)

⇒ a₇ = 7 – 28

⇒ a₇ = -21

Hence, A.P is 3, -1, -5, -9, -13, -17, -21,…