Write the first five terms of the following sequences : a1 = 1 = a2,

1.	Write the first five terms of the following sequences : a1 = 1 = a2, an = an–1 + an–2, n>2
Answer» Given, a₁ = 1 = a₂, a_n = a_n–1 + a_n–2, n>2 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 : a₁ = 1 When n = 3 : a₃ = a_3–1 + a_3–2 ⇒ a₃ = a₂ + a₁ ⇒ a₃ = 1 + 1 ⇒ a₃ = 2 When n = 4 : a₄ = a_4–1 + a_4–2 ⇒ a₄ = a₃ + a₂ ⇒ a₄ = 2 + 1 ⇒ a₄ = 3 When n = 5 : a₅ = a_5–1 + a_5–2 ⇒ a₅ = a₄ + a₃ ⇒ a₅ = 3 + 2 ⇒ a₅ = 5 ∴ First five terms of the sequence are 1, 1, 2, 3, 5.

Write the first five terms of the following sequences : a1 = 1 = a2, an = an–1 + an–2, n>2

Answer»

Given,

a₁ = 1 = a₂, a_n = a_n–1 + a_n–2, n>2

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 :

a₁ = 1

When n = 3 :

a₃ = a_3–1 + a_3–2

⇒ a₃ = a₂ + a₁

⇒ a₃ = 1 + 1

⇒ a₃ = 2

When n = 4 :

a₄ = a_4–1 + a_4–2

⇒ a₄ = a₃ + a₂

⇒ a₄ = 2 + 1

⇒ a₄ = 3

When n = 5 :

a₅ = a_5–1 + a_5–2

⇒ a₅ = a₄ + a₃

⇒ a₅ = 3 + 2

⇒ a₅ = 5

∴ First five terms of the sequence are 1, 1, 2, 3, 5.