Final answer:
The given sequence has a common difference of 600, indicating an arithmetic progression. Hence, the formula for the n-th term is 600n - 596.
Step-by-step explanation:
To determine the nth term of the given sequence 4, 604, 1204, 1804, 2404, we first need to find the pattern or rule that generates the sequence. We'll look at the differences between consecutive terms to establish a sequence's rate of change or common difference.
The differences in this sequence are 600, 600, 600, and 600, which means the sequence has a common difference of 600. This indicates that the sequence is arithmetic, and the nth term can be found using the formula for an arithmetic sequence:
an = a1 + (n - 1)d
Where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. Substituting the values into the formula:
an = 4 + (n - 1)×600
Expanding this:
an = 4 + 600n - 600
Simplifying:
an = 600n - 596
Therefore, the formula for the nth term of the sequence is 600n - 596.