Final answer:
The nth term of the sequence -9, 391, 791, 1191, 1591 can be determined using the arithmetic sequence formula T(n) = a + (n - 1)d. For this sequence, the formula simplifies to T(n) = 400n - 409.
Step-by-step explanation:
The student has provided a sequence of numbers and is seeking an expression for its nth term. To determine the nth term, a recognizable pattern needs to be found. In this sequence, each number increases by 400. Therefore, the nth term can be given by an arithmetic sequence formula:
T(n) = a + (n - 1)d
where T(n) is the nth term, a is the first term, n is the position in the sequence, and d is the common difference between the terms. Substituting the values for the given sequence (with a = -9 and d = 400), we get:
T(n) = -9 + (n - 1)*400
To simplify,
T(n) = 400n - 409
This is the formula for the nth term of the given sequence.