Write the first five terms of the following sequences : a1 = a2 = 2,

1.	Write the first five terms of the following sequences : a1 = a2 = 2, an = an–1 – 1, n>2
Answer» Given, a₁ = 2 = a₂, a_n = a_n–1 – 1, 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 = 2 When n = 2 : a₁ = 2 When n = 3 : a₃ = a_3–1 – 1 ⇒ a₃ = a₂ – 1 ⇒ a₃ = 2 – 1 ⇒ a₃ = 1 When n = 4 : a₄ = a_4–1 – 1 ⇒ a₄ = a_{3 – 1} ⇒ a₄ = 1 – 1 ⇒ a₄ = 0 When n = 5 : a₅ = a_5–1 – 1 ⇒ a₅ = a₄ – 1 ⇒ a₅ = 0 – 1 ⇒ a₅ = -1 ∴ First five terms of the sequence are 2, 2, 1, 0, -1.

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

Answer»

Given,

a₁ = 2 = a₂, a_n = a_n–1 – 1, 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 = 2

When n = 2 :

a₁ = 2

When n = 3 :

a₃ = a_3–1 – 1

⇒ a₃ = a₂ – 1

⇒ a₃ = 2 – 1

⇒ a₃ = 1

When n = 4 :

a₄ = a_4–1 – 1

⇒ a₄ = a_{3 – 1}

⇒ a₄ = 1 – 1

⇒ a₄ = 0

When n = 5 :

a₅ = a_5–1 – 1

⇒ a₅ = a₄ – 1

⇒ a₅ = 0 – 1

⇒ a₅ = -1

∴ First five terms of the sequence are 2, 2, 1, 0, -1.