Question

Let aₙ be a sequence of real numbers such that aₙ = 3aₙ₋₁ + 2, with a₁ = 2, compute a₂.

Answer 1

To calculate a₂, we use the given formula aₙ = 3aₙ₋₁ + 2 and the initial value a₁ = 2, which gives us a₂ = 8.

Step-by-step explanation:

To compute a₂, the second term of the sequence, we use the given recursive formula aₙ = 3aₙ₋₁ + 2, with a₁ = 2. We plug in the value of a₁ to find a₂:

• a₂ = 3a₁ + 2
• a₂ = 3(2) + 2
• a₂ = 6 + 2
• a₂ = 8