Question

Show that each of the following sequences is an A.P. Also, find the common difference and write 3 more terms in case. 

9, 7, 5, 3 …

Answer 1

9, 7, 5, 3 …

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,….