Final answer:
The nᵗʰ term of the sequence -3, -3.05, -3.1, -3.15, -3.2 is determined by the arithmetic sequence formula an = -2.95 - 0.05n. This sequence has a first term a1 = -3 and a common difference d = -0.05.
Step-by-step explanation:
To determine the nth term of the given sequence -3, -3.05, -3.1, -3.15, -3.2, we first need to identify the pattern of the sequence. Observing the given terms, we see that each term decreases by 0.05 from the one before. We can express this sequence algebraically as an arithmetic sequence with the first term a1 = -3 and a common difference d = -0.05.
The nth term of an arithmetic sequence is given by the formula:
an = a1 + (n - 1) × d
Substituting the values of a1 and d into the formula, we get:
an = -3 + (n - 1) × (-0.05)
Expanding and simplifying the formula:
an = -3 - 0.05n + 0.05
an = -3 + 0.05 - 0.05n
an = -2.95 - 0.05n
Therefore, the nth term of the sequence is -2.95 - 0.05n.