Question

Find the first six terms in the sequence defined by the following recursion

a₁=1, a₂=-1, aₙ+1=2 aₙ-3 aₙ-1

Answer 1

The first six terms in the sequence defined by the given recursion formula are 1, -1, -2, 4, -16, -128.

Step-by-step explanation:

To find the first six terms in the sequence defined by the recursion a₁=1, a₂=-1, aₙ+₁=2aₙ₋₃aₙ₋₁, we can use the given formula. We start with the initial terms a₁=1 and a₂=-1. Then, we apply the recursion formula to find the next terms:

1. a₃ = 2a₁a₂ = 2(1)(-1) = -2
2. a₄ = 2a₂a₃ = 2(-1)(-2) = 4
3. a₅ = 2a₃a₄ = 2(-2)(4) = -16
4. a₆ = 2a₄a₅ = 2(4)(-16) = -128

Therefore, the first six terms in the sequence are 1, -1, -2, 4, -16, -128.