Answer:
- f(1) = -24; f(n) = 4·f(n-1)
- f(1) = 13; f(n) = f(n-1) + 26
- f(1) = 28; f(n) = -4·f(n-1)
Explanation:
Identify the first term of the sequence. First terms are -24, 13, 28. Find the matching f(1). There are two choices for each first term.
Then determine the relation of each term to the previous term. In two of the sequences, a factor of 4 is involved. For the sequence starting with -24, the adjacent terms have the same sign, so the factor is +4. For the sequence starting with 28, adjacent terms have alternating signs, so the factor is -4.
For the sequence starting with 13, the second term is 3 times the first, but it is also 26 added to the first. You have to look at the next term to see if the sequence is geometric with a ratio of 3, or arithmetic with a difference of 26. The latter is the case, so the recursive definition will involve addition, not multiplication.
The recursively defined functions are shown above in the order of the given sequences.