Show that each of the following sequences is an A.P. Also, find the co

1.	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» 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,….

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»

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,….