A sequence is defined by the recursive function f(n) = f(n-1) + f(n-2). If f(1) = 10, what is f(3)?

To solve for f(3) using the recursive function f(n) = f(n-1) + f(n-2), we first need to identify the values of f(2) and f(3).

Given that f(1) = 10, we still need to find f(2). The recursive formula indicates that to find f(2), we need the values of f(1) and f(0). However, the problem does not provide f(0) directly.

For many sequences, we can assume f(0) = 0 as a starting point. Therefore, let’s assume f(0) = 0.

Now we can calculate:

• f(2) = f(1) + f(0) = 10 + 0 = 10
• f(3) = f(2) + f(1) = 10 + 10 = 20

Thus, with the assumption that f(0) is 0, we find that f(3) = 20.

Final Answer: f(3) = 20