Find the first four terms of the sequence defined by a1 = 3 and an =

1.	Find the first four terms of the sequence defined by a1 = 3 and an = 3an–1 + 2, for all n > 1.
Answer» Given as a₁ = 3 and a_n = 3a_n–1 + 2, for all n > 1 By using the values n = 1, 2, 3, 4 we can find the first four terms. Now, when n = 1: a₁ = 3 When n = 2: a₂ = 3a_2–1 + 2 = 3a₁ + 2 = 3(3) + 2 = 9 + 2 = 11 When n = 3: a₃ = 3a_3–1 + 2 = 3a₂ + 2 = 3(11) + 2 = 33 + 2 = 35 When n = 4: a₄ = 3a_4–1 + 2 = 3a₃ + 2 = 3(35) + 2 = 105 + 2 = 107 Thus, first four terms of sequence are 3, 11, 35, 107.

Find the first four terms of the sequence defined by a1 = 3 and an = 3an–1 + 2, for all n > 1.

Answer»

Given as

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

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

Now, when n = 1:

a₁ = 3

When n = 2:

a₂ = 3a_2–1 + 2

= 3a₁ + 2

= 3(3) + 2

= 9 + 2

= 11

When n = 3:

a₃ = 3a_3–1 + 2

= 3a₂ + 2

= 3(11) + 2

= 33 + 2

= 35

When n = 4:

a₄ = 3a_4–1 + 2

= 3a₃ + 2

= 3(35) + 2

= 105 + 2

= 107

Thus, first four terms of sequence are 3, 11, 35, 107.