Final answer:
The nᵗʰ term of the sequence -6, -53, -100, -147, -194 is determined by using the formula for an arithmetic sequence. The common difference is -47, and the nᵗʰ term is given by -47n + 41.
Step-by-step explanation:
To determine the nᵗʰ term of the sequence -6, -53, -100, -147, -194, we first need to find the common difference between the terms. Subtracting each term from the term that follows it, we find that the common difference is -47 (-53 - (-6) = -47, -100 - (-53) = -47, and so on).
Now that we have the common difference, we can use the formula for the nᵗʰ term of an arithmetic sequence which is:
an = a1 + (n - 1) ⋅ d
Where a1 is the first term, d is the common difference, and n is the term number.
In this sequence, a1 is -6 and d is -47. Plugging these values into the formula gives us:
an = -6 + (n - 1)(-47) = -6 - 47n + 47
Simplifying the expression leads to the nᵗʰ term formula for this sequence:
an = -47n + 41.