Final answer:
The solution to the recurrence relation is that the sequence alternates between 5 and -5. If n is even, a_n = 5, and if n is odd, a_n = -5. This is determined using an iterative approach based on the initial condition a0 = 5.
Step-by-step explanation:
The student is asking to find the solution to the recurrence relation an = –an-1 with an initial condition a0 = 5. To solve this, we apply an iterative approach where each term is the negative of the previous one.
Starting with a0 = 5, we get the following sequence of terms:
- a1 = -a0 = -5
- a2 = -a1 = 5
- a3 = -a2 = -5
- ...
This pattern will repeat with alternating signs. Hence, if n is even, an = 5, and if n is odd, an = -5.
Recurrence relations often describe sequences by defining each term in terms of the previous term(s). An iterative approach involves using the initial conditions of the sequence to generate the next terms.