College

A sequence is defined by the recursive function \( f(n + 1) = f(n) \). If \( f(3) = 9 \), what is \( f(1) \)?

A. 1
B. 3
C. 27
D. 81

Answer :

Final answer:

The recursive function given is f(n + 1) = f(n). If f(3) = 9, ƒ(1) is 9.


Explanation:

The recursive function given is f(n + 1) = f(n). This means that each term in the sequence is equal to the previous term.

If f(3) = 9, we can find f(2) by substituting n + 1 with 3 in the recursive function. So we have f(2) = f(3 - 1) = f(2) = f(2) = 9.

Similarly, we can find f(1) by substituting n + 1 with 2 in the recursive function. So f(1) = f(2 - 1) = f(1) = f(1) = 9.

Therefore, ƒ(1) is 9.

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