Question

Find the solution to the following recurrence relation with the given initial conditions:

aₙ = -a₋ₙ₋₁, a₀ = 5

Answer 1

The solution to the given recurrence relation is aₙ = 5 if n is even, and aₙ = -5 if n is odd.

Step-by-step explanation:

To find the solution to the recurrence relation aₙ = -a₋ₙ₋₁ with the initial condition a₀ = 5, we can start by listing out the terms:

• a₀ = 5
• a₁ = -a₋₁ = -a₀ = -5
• a₂ = -a₋₂ = -a₁ = 5
• a₃ = -a₋₃ = -a₂ = -5
• ...

From this pattern, we can see that the terms alternate between 5 and -5. Therefore, the solution to the recurrence relation is:

aₙ = 5 if n is even

aₙ = -5 if n is odd