Answer:

(i)

Using n = 1, 2, 3, 4, 5, the first five terms can be calculated.

If n = 1,

a₁ = 1

If n = 2,

a₂ = a_2–1 + 2

a₂ = a₁ + 2

a₂ = 1 + 2

a₂ = 3

If n = 3,

a₃ = a_3–1 + 2

a₃ = a₂ + 2

a₃ = 3 + 2

a₃ = 5

If n = 4,

a₄ = a_4–1 + 2

a₄ = a₃ + 2

a₄ = 5 + 2

a₄ = 7

If n = 5,

a₅ = a_5–1 + 2

a₅ = a₄ + 2

a₅ = 7 + 2

a₅ = 9

∴ First five terms of the sequence are 1, 3, 5, 7, 9.

(ii)

Using n = 1, 2, 3, 4, 5, the first five terms can be calculated.

If n = 1,

a₁ = 1

If n = 2,

a₂ = 1

If n = 3,

a₃ = a_3–1 + a_3–2

a₃ = a₂ + a₁

a₃ = 1 + 1

a₃ = 2

If n = 4,

a₄ = a_4–1 + a_4–2

a₄ = a₃ + a₂

a₄ = 2 + 1

a₄ = 3

If n = 5,

a₅ = a_5–1 + a_5–2

a₅ = a₄ + a₃

a₅ = 3 + 2

a₅ = 5

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