Final answer:
The nᵗʰ term of the sequence 15, -30, -75, -120, -165 is determined by identifying it as an arithmetic sequence and applying the nth term formula Tn = a1 + (n - 1) × d, which results in Tn = 60 - 45n.
Step-by-step explanation:
To determine the nᵗʰ term of the given sequence 15, -30, -75, -120, -165, let's first observe the pattern between consecutive terms.
The difference between consecutive terms is as follows:
Since the common difference is consistent, we're dealing with an arithmetic sequence. The nth term of an arithmetic sequence is given by:
Tn = a1 + (n - 1) × d
Where Tn is the nth term, a1 is the first term and d is the common difference. Plugging our values in,
Tn = 15 + (n - 1) × (-45)
Simplify to:
Tn = 15 - 45n + 45
So,
Tn = 60 - 45n
Therefore, the nth term of the sequence is 60 - 45n.