Write the first five terms of the following sequences : a1 = 1, an =

1.	Write the first five terms of the following sequences : a1 = 1, an = an–1 + 2, n > 1
Answer» Given, a₁ = 1, a_n = a_n–1 + 2, n > 1 We can find the first five terms of a sequence by putting values of n From 1 to 5 When n = 1 : a₁ = 1 When n = 2 : a₂ = a_2–1 + 2 ⇒ a₂ = a₁ + 2 ⇒ a₂ = 1 + 2 ⇒ a₂ = 3 When n = 3 : a₃ = a_3–1 + 2 ⇒ a₃ = a₂ + 2 ⇒ a₃ = 3 + 2 ⇒ a₃ = 5 When n = 4 : a₄ = a_4–1 + 2 ⇒ a₄ = a₃+ 2 ⇒ a₄ = 5 + 2 ⇒ a₄ = 7 When n = 5 : a₅ = a_5–1 + 2 ⇒ a₅ = a₄+ 2 ⇒ a₅ = 7 + 2 ⇒ a₅ = 9 ∴ First five terms of the sequence are 1, 3, 5, 7, 9.

Write the first five terms of the following sequences : a1 = 1, an = an–1 + 2, n > 1

Answer»

Given,

a₁ = 1,

a_n = a_n–1 + 2, n > 1

We can find the first five terms of a sequence by putting values of n

From 1 to 5

When n = 1 :

a₁ = 1

When n = 2 :

a₂ = a_2–1 + 2

⇒ a₂ = a₁ + 2

⇒ a₂ = 1 + 2

⇒ a₂ = 3

When n = 3 :

a₃ = a_3–1 + 2

⇒ a₃ = a₂ + 2

⇒ a₃ = 3 + 2

⇒ a₃ = 5

When n = 4 :

a₄ = a_4–1 + 2

⇒ a₄ = a₃+ 2

⇒ a₄ = 5 + 2

⇒ a₄ = 7

When n = 5 :

a₅ = a_5–1 + 2

⇒ a₅ = a₄+ 2

⇒ a₅ = 7 + 2

⇒ a₅ = 9

∴ First five terms of the sequence are 1, 3, 5, 7, 9.