Final answer:
The function f(n) = f(n-1) + 5 with the initial term f(n) = 4 is an arithmetic sequence because it adds a constant value (5) to each term to obtain the next. It's presented in a recursive form since each term is defined using the previous term. The correct classification is Arithmetic, Recursive.
Step-by-step explanation:
The question asks to classify the function f(n) = 4, f(n) = f(n-1) + 5 according to its type and formula representation. This function is an arithmetic sequence because the same number (5) is added to each term to get the next term in the sequence. The given initial condition, f(n) = 4, provides the first term. From the recursive formula f(n) = f(n-1) + 5, each subsequent term is found by adding 5 to the previous term, which confirms the arithmetic nature of the sequence. Therefore, the sequence is not geometric since it does not involve multiplying a constant ratio. It is a recursive formula because each term is defined based on the preceding term.
The function is given in a recursive form rather than an explicit form. An explicit form would not require the computation of the previous terms to find the value of f(n). Therefore, the correct answer is Arithmetic, Recursive, which corresponds to the choice (A).