Final answer:
The question involves solving a linear recurrence relation with an initial condition. Assuming the 'P' in the question is a typo, the corrected relation is A(n) = 2A(n-1) + n2^n. The solution requires recursive calculation of each term using the previous term.
Step-by-step explanation:
The student is asking to solve the recurrence relation A(n) = 2A(n-1) + n2^n with the initial condition A(1) = 2 for n ≥ 2. There seems to be some confusion regarding the use of 'P' in the given recurrence relation, as it is not defined within the question. Assuming 'P' was a typo and should actually be 'A', the relation becomes A(n) = 2A(n-1) + n2^n, which is a non-homogeneous linear recurrence relation. To solve this, we look for a particular solution to the non-homogeneous part and then find the homogenous solution. The initial condition helps establish the base case for recursive calculation.
The recurrence relation suggests that every term depends on the previous term multiplied by 2, plus an additional term that is a product of n and 2 raised to the power of n. Without a closed-form expression, the solution would involve iteratively calculating each term based on the previous term according to the given recurrence.