Final answer:
The nᵗʰ term of the sequence is found by using the formula for an arithmetic sequence, which is -300n + 306.
Step-by-step explanation:
To find the nᵗʰ term of the given sequence 6, -294, -594, -894, -1194, we first determine the pattern of the sequence. The difference between consecutive terms is -300, indicating that this is an arithmetic sequence.
The general formula for the nᵗʰ term of an arithmetic sequence is aₙ = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference. In this case, a₁ = 6 and d = -300. Substituting these values into the formula gives us:
aₙ = 6 + (n - 1)(-300)
aₙ = 6 - 300n + 300
aₙ = -300n + 306
Therefore, the nᵗʰ term of the sequence is -300n + 306.