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

a₁ = 9, a₂ = 7, a₃ = 5, a₄ = 3

Now, a₂ – a₁ = 7 – 9 = -2

a₃ – a₂ = 5 – 7 = -2

a₄ – a₃ = 3 – 5 = -2

As, a₂ – a₁ = a₃ – a₂ = a₄ – a₃

The given sequence is A.P

Common difference, d = a₂ – a₁ = -2

To find the 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 = 9 + (n-1) -2

⇒ a_n = 9 – 2n + 2

⇒ a_n = 11 – 2n

When n = 5:

a₅ = 11 – 2(5)

⇒ a₅ = 11 – 10

⇒ a₅ = 1

When n = 6:

a₆ = 11 – 2(6)

⇒ a₆ = 11 – 12

⇒ a₆ = -1

When n = 7:

a₇ = 11 – 2(7)

⇒ a₇ = 11 – 14

⇒ a₇ = -3

Hence, A.P is 9, 7, 5, 3, 1, -1, -3,….