Question

A sequence is defined recursively using the formula . If the first term of the sequence is 120, what is f(5)?

−15
−7.5
7.5
15

Answer 1

To solve this problem, we need to determine the recursive formula and apply it to find the fifth term of the sequence given that the first term \( f(1) \) is 120. Unfortunately, the exact recursive formula is not provided in the question, so let's assume a typical type of recursion that could apply.

One common type of recursive formula is:
\[ f(n+1) = \frac{1}{2} f(n) \]

Using this formula:
1. **Given**: \( f(1) = 120 \)
2. Compute \( f(2) \):
\[ f(2) = \frac{1}{2} f(1) = \frac{1}{2} \times 120 = 60 \]
3. Compute \( f(3) \):
\[ f(3) = \frac{1}{2} f(2) = \frac{1}{2} \times 60 = 30 \]
4. Compute \( f(4) \):
\[ f(4) = \frac{1}{2} f(3) = \frac{1}{2} \times 30 = 15 \]
5. Compute \( f(5) \):
\[ f(5) = \frac{1}{2} f(4) = \frac{1}{2} \times 15 = 7.5 \]

Thus, \( f(5) \) would be \( 7.5 \) under this assumption.

Given these steps lead us to the answer, the correct choice is:

\[ \boxed{7.5} \]