Question

a. find all solutions of the recurrence relation an = 2an−1 2n2. b. find the solution of the recurrance relation in part (a) with initial condition a1 = 4.

Answer 1

The recurrence relation an = 2an−1 × 2n² can be solved by iterative substitution using the initial condition a1 = 4. Starting with a1 = 4, the next terms a2, a3, etc., are found by repeatedly applying the recurrence relation, yielding a2 = 32, a3 = 512, and so on.

Step-by-step explanation:

The recurrence relation given by an = 2an−1 × 2n² can be solved by establishing a pattern through iterative substitution starting from the initial condition. To find the solution to this recurrence relation with the initial condition a1 = 4, we simply apply the recurrence relation:

• a2 = 2a1 × 2² = 2(4) × 4 = 32
• a3 = 2a2 × 2³ = 2(32) × 8 = 512

And so on. The general formula for the nth term would involve repeated multiplication based on the pattern observed. Unfortunately, without the full view of the standard form of the recurrence relation, we cannot provide comprehensive steps to derive a closed-form solution.