The sequence an is defined by a0 = 1 and an = 2an-1 + 2 for n ≥ 0. What is the value of a3?

To find the value of a₃, we first need to calculate the earlier terms of the sequence based on the definition provided.

1. Given that a₀ = 1.

2. Now, let’s find a₁:
a₁ = 2a₀ + 2 = 2(1) + 2 = 2 + 2 = 4.

3. Next, we calculate a₂:
a₂ = 2a₁ + 2 = 2(4) + 2 = 8 + 2 = 10.

4. Finally, we compute a₃:
a₃ = 2a₂ + 2 = 2(10) + 2 = 20 + 2 = 22.

Thus, the value of a₃ is 22.