Final answer:
To determine the nᵗʰ term of the sequence -2, -9.2, -16.4, -23.6, -30.8, we use the common difference of -7.2 and the first term of -2 to derive the formula for the nᵗʰ term, which is -7.2n + 5.2.
Step-by-step explanation:
To find the nᵗʰ term of the given sequence -2, -9.2, -16.4, -23.6, -30.8, we will first determine the common difference between the terms. By subtracting any term from the preceding term, we find that the common difference is -7.2. We can write the nᵗʰ term of an arithmetic sequence with the following formula:
aₙ = a₁ + (n - 1)d
where aₙ is the nᵗʰ term, a₁ is the first term, d is the common difference, and n is the term number. Using the given sequence, a₁ is -2, and d is -7.2. So, the formula for this sequence's nᵗʰ term is:
aₙ = -2 + (n - 1)(-7.2)
By expanding the formula, we get:
aₙ = -2 - 7.2n + 7.2
aₙ = -7.2n + 5.2
Therefore, the nᵗʰ term of the sequence is -7.2n + 5.2.