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 each case. 3, -1, -5, -9…
Answer» 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 – 4_n 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,…

Show that each of the following sequences is an A.P. Also, find the common difference and write 3 more terms in each case. 3, -1, -5, -9…

Answer»

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 – 4_n

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,…