Final answer:
The nth term of the sequence 15, -15, -45, -75, -105 can be found using the formula an = 15 - 30(n - 1), where an represents the nth term of the sequence.
Step-by-step explanation:
The student is looking to determine the nᵗʰ term of the sequence 15, -15, -45, -75, -105. To find the nᵗʰ term, we first observe the pattern in the sequence. We can see that each term is decreasing by 30 more than the previous one.
Let's denote the nᵗʰ term by aₙ. The sequence starts at 15 and subtracts 30 each time we move to the next term. Therefore, the nᵗʰ term can be calculated using the formula:
aₙ = 15 - 30(n - 1)
This is because the first term a₁ is 15, and for each subsequent term, we subtract 30 times the (position - 1). For example, the second term (n=2) should be:
a₂ = 15 - 30(2 - 1) = 15 - 30 = -15
Following this pattern, we can calculate any nᵗʰ term of the sequence.