Question

Arrange the following steps of the recurrence relation an = an – 1 – n with the initial condition a0 = 4.

Answer 1

To arrange the steps of the recurrence relation an = an – 1 – n with the initial condition a0 = 4, start by calculating the first few terms of the sequence.

Step-by-step explanation:

To arrange the steps of the recurrence relation an = an – 1 – n, we start with the initial condition a0 = 4. Let's calculate the first few terms:

1. a0 = 4
2. a1 = a0 - 1 - 1 = 4 - 1 - 1 = 2
3. a2 = a1 - 2 - 2 = 2 - 2 - 2 = -2
4. a3 = a2 - 3 - 3 = -2 - 3 - 3 = -8
5. a4 = a3 - 4 - 4 = -8 - 4 - 4 = -16

So, the arrangement of the steps of the recurrence relation with the initial condition a0 = 4 is: 4, 2, -2, -8, -16, ...