Final answer:
The nth term of the given sequence is determined by the formula T(n) = -7 for n = 1, and T(n) = 993 + 1000(n - 2) for all n > 1, which identifies the pattern in the sequence.
Step-by-step explanation:
To determine the nth term of the sequence -7, 993, 1993, 2993, 3993, we can first observe the pattern that each term increases by 1000 from the second term onwards. Thus, the sequence appears to have a starting term and then follows a linear pattern with a common difference. The first term, which is not conforming to the linear pattern, can be considered as an outlier.
The linear sequence starts at 993, so if we subtract 1000 from 993 we get -7, which is the first term. Therefore, the linear progression that starts with 993 can be defined by the general term 993 + 1000(n-2), where n is the position of the term in the sequence starting from the term 993. To make n correspond to the entire sequence including the first term, our formula will become:
T(n) = 993 + 1000(n - 2) for all n > 1.
For n = 1 (the first term), T(n) = -7 because it doesn't follow the pattern established by the rest.
In conclusion, the nth term of the sequence can be defined as follows:
- For n = 1, T(n) = -7
- For n > 1, T(n) = 993 + 1000(n - 2)