Find the first fo

Given,

a₁ = 3 and a_n = 3a_n–1 + 2, for all n > 1

We can find the first four terms of a sequence by putting values of n

from 1 to 4

When n = 1:

a₁ = 3

When n = 2:

a₂ = 3a_2–1 + 2

⇒ a₂ = 3a₁ + 2

⇒ a₂ = 3(3) + 2

⇒ a₂ = 9 + 2

⇒ a₂ = 11

When n = 3:

a₃ = 3a_3–1 + 2

⇒ a₃ = 3a₂ + 2

⇒ a₃ = 3(11) + 2

⇒ a₃ = 33 + 2

⇒ a₃ = 35

When n = 4:

a₄ = 3a_4–1 + 2

⇒ a₄ = 3a₃ + 2

⇒ a₄ = 3(35) + 2

⇒ a₄ = 105 + 2

⇒ a₄ = 107

∴ First four terms of sequence are 3, 11, 35, 107.