The Fibonacci sequence is defined by a 1 = 1 = a 2 , a n = a n–1 + a n–2 for n > 2. Find for n = 1, 2, 3, 4, 5.

The Fibonacci sequence is defined by a₁ = 1 = a₂, a_n = a_n–1 + a_n–2for n > 2. Find for n = 1, 2, 3, 4, 5.

Given: a₁ = 1 = a₂, a_n = a_n–1 + a_n–2, n>2

When n = 1:

a₃ = a_3–1 + a_3–2

⇒ a₃ = a₂ + a₁

⇒ a₃ = 1 + 1

⇒ a₃ = 2

When n = 2:

a₄ = a_4–1 + a_4–2

⇒ a₄ = a₃ + a₂

⇒ a₄ = 2 + 1

⇒ a₄ = 3

When n = 3:

a₅ = a_5–1 + a_5–2

⇒ a₅ = a₄ + a₃

⇒ a₅ = 3 + 2

⇒ a₅ = 5

When n = 4:

a₆ = a_6–1 + a_6–2

⇒ a₆ = a₅ + a₄

⇒ a₆ = 5 + 3

⇒ a₆ = 8

When n = 5:

5