Question

List the first 9 terms of the sequence defined recursively by (aₙ = -2 ⋅ (aₙ₋₁ + 1)), with (a₁ = 2) and (a₂ = 3).

a. -2, 0, -4, -6, -8, -10, -12, -14, -16
b. 2, 0, -2, -4, -6, -8, -10, -12, -14
c. 2, 6, 8, 12, 14, 18, 20, 24, 26
d. -2, 6, 8, 12, 14, 18, 20, 24, 26

Answer 1

The first 9 terms of the sequence defined recursively are: 2, 3, -8, 15, -32, 66, -134, 270, -542.

Step-by-step explanation:

To list the first 9 terms of the sequence defined recursively by (aₙ = -2 ⋅ (aₙ₋₁ + 1)), with (a₁ = 2) and (a₂ = 3), we can follow these steps:

1. a₁ = 2 (given)
2. a₂ = 3 (given)
3. a₃ = -2 ⋅ (a₂ + 1) = -2 ⋅ (3 + 1) = -8
4. a₄ = -2 ⋅ (a₃ + 1) = -2 ⋅ (-8 + 1) = 15
5. a₅ = -2 ⋅ (a₄ + 1) = -2 ⋅ (15 + 1) = -32
6. a₆ = -2 ⋅ (a₅ + 1) = -2 ⋅ (-32 + 1) = 66
7. a₇ = -2 ⋅ (a₆ + 1) = -2 ⋅ (66 + 1) = -134
8. a₈ = -2 ⋅ (a₇ + 1) = -2 ⋅ (-134 + 1) = 270
9. a₉ = -2 ⋅ (a₈ + 1) = -2 ⋅ (270 + 1) = -542

Therefore, the first 9 terms of the sequence are: 2, 3, -8, 15, -32, 66, -134, 270, -542.