Question

Identify the first five terms of the sequence in which a1 = 3 and an = 4an−1− 5 for n ≥ 2.

Answer 1

3, 7, 23, 87, 343

Explanation:

Using the recursive rule and a₁ = 3 , then

a₂ = 4a₁ - 5 = 4(3) - 5 = 12 - 5 = 7

a₃ = 4a₂ - 5 = 4(7) - 5 = 28 - 5 = 23

a₄ = 4a₃ - 5 = 4(23) - 5 = 92 - 5 = 87

a₅ = 4a₄ - 5 = 4(87) - 5 = 348 - 5 = 343

Answer 2

Explanation:

a1 = 3

an = 4an-1 - 5

a2 = 4×3 - 5 = 12 - 5 = 7

a3 = 4×7 - 5 = 28 - 5 = 23

a4 = 4×23 - 5 = 92 - 5 = 87

a5 = 4×87 - 5 = 348 - 5 = 343