t₁ = 1

t₂ = 1

t_n = t_n-2 + t_n-1

Knowing that the first term is one and the second term is one (t₁ = 1 and t₂ = 1), calculate the value of the third term (t₃)

Since we need to calculate t₃, substitute n = 3 into the third part of the recursive rule (t_n = t_n-2 + t_n-1)

      t₍₃₎ = t_(3)-2 + t_(3)-1

      t₃ = t₁ + t₂                  (But it is known that t₁ = 1 and t₂ = 1)

      t₃ = 1 + 1

      t₃ = 2

Repeat this process to find t₄.

Knowing that the first three terms are one, one and two (t₁ = 1, t₂ = 1 and t₃ = 2) calculate the value of the fourth term (t₄)

Since we need to calculate t₄, substitute n = 4 into the third part of the recursive rule (t_n = t_n-2 + t_n-1)

      t₍₄₎ = t_(4)-2 + t_(4)-1

      t₄ = t₂ + t₃                  (But it is known that t₂ = 1 and it was calculated that t₃ = 2)

      t₄ = 1 + 2

      t₄ = 3

Repeat this process to find t₅.

Knowing that the first four terms are one, one, two and three (t₁ = 1, t₂ = 1, t₃ = 2 and t₄ = 3) calculate the value of the fifth term (t₅)

Since we need to calculate t₅, substitute n = 5 into the third part of the recursive rule (t_n = t_n-2 + t_n-1)

      t₍₅₎ = t_(5)-2 + t_(5)-1

      t₅ = t₃ + t₄                  (But it was calculated that t₃ = 2 and t₄ = 3)

      t₅ = 2 + 3

      t₅ = 5

Repeat this process to find as many terms as required.

Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .

Sequence: Starting with one and one, add two succesive terms of the sequence to determine the next term of the sequence.