Question

Find the solution of the recurrence relation an = 3an-1, with a0 = 2.

a) 2 * 3ⁿ
b) 2ⁿ * 3
c) 3ⁿ
d) 3(n+1)

Answer 1

The solution of the recurrence relation an = 3an-1 with a0 = 2 is found iteratively, and the correct answer matches option (a), which is 2 * 3^n.

Step-by-step explanation:

The solution to the recurrence relation an = 3an-1 with an initial condition of a0 = 2 can be found by iterating the relation starting from n=0. Let's do this step-by-step:

1. For n=1, a1 = 3 * a0 = 3 * 2 = 6.
2. For n=2, a2 = 3 * a1 = 3 * 6 = 18, which is 2 * 3^2.
3. Observing the pattern, an = 2 * 3^n seems to satisfy the given recurrence relation, as each term is three times the previous term and started with 2 when n=0.
4. Therefore, the correct answer is option (a) 2 * 3^n.