Final answer:
The recursive definition for the arithmetic sequence that starts with 2, 5 is f(1) = 2, and f(n) = f(n-1) + 3 for n > 1, where f(n) is the nth term and f(n-1) is the previous term in the sequence.
Step-by-step explanation:
To write a recursive definition for the given arithmetic sequence starting with 2, 5, we first need to determine the common difference between consecutive terms. As we can see, the difference between the second term (5) and the first term (2) is 3. This common difference of 3 will be added to each term to get the next term in the sequence.
The recursive formula for an arithmetic sequence can be expressed using function notation as f(n) = f(n-1) + d, where f(n) is the term we want to find, f(n-1) is the previous term, and d is the common difference.
So, in this case, the recursive definition would look like this:
- f(1) = 2,
- f(n) = f(n-1) + 3 for n > 1.
This means that to find any term in the sequence, you take the previous term and add 3 to it.