Final answer:
To determine the nth term of the sequence 0, 2, 4, 6, 8, and so on, the function f(n) can be written as f(n) = 2(n - 1). This formula correctly calculates each term of the sequence by multiplying the term number by 2 and then subtracting 2 to align with the sequence starting at 0 for n=1.
Step-by-step explanation:
The student's question involves creating a function f(n) that describes the nth term of the given arithmetic sequence 0, 2, 4, 6, 8, and so on. Each term increases by 2, starting from 0 for the first term. Therefore, the function that represents the nth term of the sequence is f(n) = 2(n - 1) because when n=1 (the first term), f(1) = 2(1 - 1) = 0, which corresponds to the given sequence.
Another way to approach this is by recognizing the pattern of even numbers starting from 0. The nth even number can be obtained by multiplying n by 2, but since we start from zero (as indicated by f(1)=0), we must subtract 1 from n before the multiplication: f(n) = 2 * (n - 1).