(i) a₁ = 1, a_n = a_n–1 + 2, n > 1

By using the values n = 1, 2, 3, 4, 5 we can find that the first five terms.

Given as

a₁ = 1

Now, when n = 2:

a₂ = a_2–1 + 2

= a₁ + 2

= 1 + 2

= 3

When n = 3:

a₃ = a_3–1 + 2

= a₂ + 2

= 3 + 2

= 5

When n = 4:

a₄ = a_4–1 + 2

= a₃ + 2

= 5 + 2

= 7

When n = 5:

a₅ = a_5–1 + 2

= a₄ + 2

= 7 + 2

= 9

Thus, first five terms of the sequence are 1, 3, 5, 7, 9.

(ii) a₁ = 1 = a₂, a_n = a_n–1 + a_n–2, n > 2

By using the values n = 1, 2, 3, 4, 5 we can find the first five terms.

Given as

a₁ = 1

a₂ = 1

When n = 3:

a₃ = a_3–1 + a_3–2

= a₂ + a₁

= 1 + 1

= 2

When n = 4:

a₄ = a_4–1 + a_4–2

= a₃ + a₂

= 2 + 1

= 3

When n = 5:

a₅ = a_5–1 + a_5–2

= a₄ + a₃

= 3 + 2

= 5

Thus, first five terms of the sequence are 1, 1, 2, 3, 5.

(iii) a₁ = a₂ =2, a_n = a_n–1 – 1, n > 2

By using the values n = 1, 2, 3, 4, 5 we can find the first five terms.

Given as

a₁ = 2

a₂ = 2

When n = 3:

a₃ = a_3–1 – 1

= a₂ – 1

= 2 – 1

= 1

When n = 4:

a₄ = a_4–1 – 1

= a₃ – 1

= 1 – 1

= 0

When n = 5:

a₅ = a_5–1 – 1

= a₄ – 1

= 0 – 1

= -1

Thus, first five terms of the sequence are 2, 2, 1, 0, -1.