Final answer:
To find the nᵗʰ term of the sequence 7, 407, 807, 1207, 1607, we use the formula for an arithmetic sequence, Tₙ = a + (n - 1)d, which yields Tₙ = 400n - 393 as the nᵗʰ term formula.
Step-by-step explanation:
The student's question involves finding the nᵗʰ term of the given sequence: 7, 407, 807, 1207, 1607. Looking at the sequence, we see that the difference between consecutive terms is 400.
This indicates that the sequence is arithmetic with a common difference (d) of 400. To determine the nᵗʰ term formula for an arithmetic sequence, we use the formula: Tₙ = a + (n - 1)d, where Tₙ is the n-th term, a is the first term, n is the term number, and d is the common difference.
In this sequence, the first term a is 7, and the common difference d is 400. Plugging these values into the formula gives us: Tₙ = 7 + (n - 1)400. Simplifying this gives us the nᵗʰ term as Tₙ = 400n - 393.