Question

Find the solution to the recurrence relation an = 3an-1 with initial condition a0 = 2 using an iterative approach.

Answer 1

To find the solution to the recurrence relation an = 3an-1 with initial condition a0 = 2 using an iterative approach, we can compute the values of an for each value of n. The first term is 2, and each subsequent term is found by multiplying the previous term by 3. Hence, the solution is a0 = 2, a1 = 6, a2 = 18, a3 = 54, and so on.

Step-by-step explanation:

To find the solution to the recurrence relation an = 3an-1 with initial condition a0 = 2 using an iterative approach, we can start by computing the values of an for each value of n.

1. Since we are given a0 = 2, we know the first term in the sequence is 2.
2. To find the second term, we substitute n = 1 into the recurrence relation: a1 = 3a0 = 3(2) = 6.
3. We continue this process for each subsequent term, using the previous term in the formula: a2 = 3a1 = 3(6) = 18, a3 = 3a2 = 3(18) = 54, and so on.

Therefore, the solution to the recurrence relation an = 3an-1 with initial condition a0 = 2 using an iterative approach is a0 = 2, a1 = 6, a2 = 18, a3 = 54, and so on.