Final answer:
To find the explicit formula for a given recursive sequence, one must express the n-th term directly. Using algebra to simplify each provided option, expressions for f(n) are obtained. Without additional information such as initial condition, it is impossible to determine which option correctly represents the sequence.
Step-by-step explanation:
To identify the explicit formula for the sequence given by the recursive formula, we need to find a formula that expresses the n-th term f(n) without the need for the previous term. Let's analyze each option provided:
- A) f(n)=4–2(n–1): This option can be simplified to f(n) = 4 - 2n + 2 which simplifies further to f(n) = 6 - 2n.
- B) f(n)=-2+4(n–1): This simplifies to f(n) = -2 + 4n - 4, and then to f(n) = 4n - 6.
- C) f(n)=-4+2(n–1): After simplification, this becomes f(n) = -4 + 2n - 2, which is f(n) = 2n - 6.
- D) f(n)=2–4(n–1): Simplifying yields f(n) = 2 - 4n + 4, and further simplification gives f(n) = 6 - 4n.
To decide amongst these options, we would typically look at initial conditions or other information given by the recursive definition, which is not provided here. If we were given an initial condition, like f(1), we could substitute n=1 in each of these expressions to see which one matches the initial term of the sequence. Without further information, we cannot definitively choose an option.