Final answer:
The equation representing the nth term of the sequence {2, -1, -4, -7, ...} is an = 5 - 3n, where an is the nth term and n is the position of the term in the sequence.
Step-by-step explanation:
To find the equation that represents the nth term of the sequence {2, -1, -4, -7, ...}, we need to determine the pattern of the sequence. We can see that each term is decreasing by 3 from the previous term. This indicates a common difference, which is characteristic of an arithmetic sequence.
The nth term of an arithmetic sequence can be found using the formula 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 between the terms. In this sequence, a1 = 2 and d = -3.
Therefore, substituting the values into the formula gives us an = 2 + (n - 1)(-3). Simplifying, the equation for the nth term is an = 5 - 3n.