Final answer:
The nᵗʰ term of the arithmetic sequence 3, -297, -597, -897, -1197 is determined using the formula Tₙ = a + (n - 1)d, where a is the first term and d is the common difference. The answer is Tₙ = -300n + 303.
Step-by-step explanation:
The question asks to determine the nᵗʰ term of the given sequence: 3, -297, -597, -897, -1197. To find the nᵗʰ term, first, let's observe the pattern in the sequence. The difference between successive terms is constant, indicating that this is an arithmetic sequence. The common difference is found by subtracting any term from the one that follows it:
-297 - 3 = -300
-597 - (-297) = -300
This pattern continues, so the common difference (d) is -300.
The formula for the nᵗʰ term (Tₙ) of an arithmetic sequence is:
Tₙ = a + (n - 1)d
where a is the first term and d is the common difference.
Thus, for this sequence:
Tₙ = 3 + (n - 1)(-300)
Tₙ = 3 - 300n + 300
Tₙ = -300n + 303
This formula can be used to find any term of the sequence by substituting the desired value of n.