Question

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

Answer 1

5, 7, 11, 19, 35

Explanation:

Using the recursive formula and a₁ = 5 , then

a₂ = 2a₁ - 3 = (2 × 5) - 3 = 10 - 3 = 7

a₃ = 2a₂ - 3 = (2 × 7) - 3 = 14 - 3 = 11

a₄ = 2a₃ - 3 = (2 × 11) - 3 = 22 - 3 = 19

a₅ = 2a₄ - 3 = (2 × 19) - 3 = 38 - 3 = 35

Thus the first 5 terms are

5, 7, 11, 19, 35