Final answer:
The recursive functions provided do not match all the sequences accurately. Sequence B matches the function f(n) = f(n-1) + 26 and Sequence D is the same as B; the other functions do not produce the sequences listed as A and C.
Step-by-step explanation:
The question requires matching each given sequence to its appropriate recursively defined function. Let's examine each sequence:
- Sequence A: – Using the given sequence (-24, -96, -384, -1,536, ...), we can see that each term is multiplied by 4 to obtain the next term. However, the recursively defined function f(n) = 4 - f(n-1) would not generate this sequence since subtracting the previous term from 4 would not produce the terms given.
- Sequence B: – In the sequence (13, 39, 65, 91, ...), the pattern is that each term is 26 more than the previous term. Therefore, the correct recursive function is f(n) = f(n-1) + 26.
- Sequence C: – Looking at the sequence (28, -112, 448, -1,792, ...), we notice that each term is -4 times the previous term, which is not captured by the function f(n) = f(n-1) - 84.
- Sequence D: – The sequence (13, 39, 65, 91, ...) is identical to Sequence B and thus has the same recursive function f(n) = f(n-1) + 26, not the function f(n) = 3 × f(n-1).
None of the provided sequences match the functions f(n) = 4 - f(n-1) and f(n) = f(n-1) - 84 exactly. To match Sequence A correctly, we need a function like f(n) = 4 × f(n-1), and for Sequence C, a function like f(n) = -4 × f(n-1) would be appropriate.