Question

Which recursive sequence would produce the sequence 6 , − 8 , 20

Answer 1

Below

Explanation:

There are many possible recursive sequences that could generate the sequence 6, -8, 20. Here is one possible example:

Let a₀ = 6, a₁ = -8, a₂ = 20

Then, for n ≥ 2:aₙ = 2aₙ₋₁ - 3aₙ₋₂ + 4aₙ₋₃

Using this formula, we can generate the sequence as follows:

a₃ = 2a₂ - 3a₁ + 4a₀ = 2(20) - 3(-8) + 4(6) = 72

a₄ = 2a₃ - 3a₂ + 4a₁ = 2(72) - 3(20) + 4(-8) = 94

a₅ = 2a₄ - 3a₃ + 4a₂ = 2(94) - 3(72) + 4(20) = 6

Therefore, the recursive sequence that produces the sequence 6, -8, 20 is:

a₀ = 6, a₁ = -8, a₂ = 20, and for n ≥ 2:

aₙ = 2aₙ₋₁ - 3aₙ₋₂ + 4aₙ₋₃