Question

Which recursive sequence would produce the sequence 9, −41, 159,...?

a. a₁=9 and aₙ=4aₙ₋₁-5
b. a₁=9 and aₙ=-5aₙ₋₁+4
c. a₁=9 and aₙ=-4aₙ₋₁-5
d. a₁=9 and aₙ=-5aₙ₋₁-4

Answer 1

The recursive sequence that would produce the given sequence is option (c) a₁=9 and aₙ=-4aₙ₋₁-5.

Step-by-step explanation:

The recursive sequence that would produce the given sequence is option (c) a₁=9 and aₙ=-4aₙ₋₁-5.

To generate the sequence, each term is obtained by multiplying the previous term by -4 and then subtracting 5. For example, starting with a₁=9:

1. a₂ = -4(9) - 5 = -41
2. a₃ = -4(-41) - 5 = 159

This pattern continues for the rest of the sequence.