Final answer:
The student's mathematics question involves solving two types of recursive sequences, linear and division-based. The first requires straightforward calculation using the previous term and the second involves evaluating when the input is a power of four. Both necessitate a step-by-step approach to determine the sequence's terms.
Step-by-step explanation:
The student's question requires solving two recursive sequences, each defining x(n) in a different manner, which is a concept in mathematics. The sequence in part (a) is linear recursive, while the sequence in part (b) has a recursive relation that involves dividing the argument by 4. The solving process might incorporate different methods, including direct computation, finding a pattern, and the use of series expansions.
Solving the first sequence involves calculating each term based on the previous one and adding the index of the term. As an example, x(2) would be 3x(1) + 2, where x(1) is given as 4; hence, x(2) would be 14. This process is repeated for additional terms like x(3), x(4), etc., building upon the previous values.
The second sequence requires a bit more thought. For n=4ᵏ, the function simplifies since x(n/4) would be x(4ᵏ-1), and that is the same as x(n) if n is a power of 4. In this manner, we can solve for terms where n is a power of 4 and then build additional terms from those key values.