Final answer:
The nth term of the sequence -7, -907, -1807, -2707, -3607 can be determined using the formula for the nth term of an arithmetic sequence. The common difference is -900, and the nth term formula is an = 893 - 900n.
Step-by-step explanation:
To find the nᵗʰ term of the given sequence -7, -907, -1807, -2707, -3607, we need to determine the pattern. The sequence decreases by 900 each time; for instance, -907 - (-7) = -900, -1807 - (-907) = -900, and so on. This pattern suggests that the sequence is arithmetic with a common difference of -900.
The nᵗʰ term of an arithmetic sequence is given by 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. For this sequence, a1 = -7 and d = -900.
Therefore, the nᵗʰ term can be calculated as:
an = -7 + (n - 1)(-900)
an = -7 - 900n + 900
an = 893 - 900n
So, the formula for the nᵗʰ term is an = 893 - 900n.