Final answer:
The nᵗʰ term of the arithmetic sequence with the first term of 18 and the second term of -582 is calculated using the formula aₙ = a₁ + (n - 1)d. The common difference (d) is found to be -600, leading to the nᵗʰ term formula aₙ = 618 - 600n.
Step-by-step explanation:
The student is asking for the nᵗʰ term of an arithmetic sequence where the first term is 18 and the second term is -582. To find the nᵗʰ term of an arithmetic sequence, the formula used is 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 between terms.
To determine the common difference (d), we subtract the first term from the second term:
d = a₂ - a₁
d = (-582) - 18
d = -600
Now we can find the nᵗʰ term using the formula:
aₙ = 18 + (n - 1)(-600)
aₙ = 18 - 600n + 600
aₙ = 618 - 600n
So the nᵗʰ term of this arithmetic sequence is 618 - 600n.