Final answer:
The nᵗʰ term of the arithmetic sequence with a third term of -1592 and a fifth term of -3192 is found using the common difference and the first term.
Step-by-step explanation:
To determine the nth term of an arithmetic sequence, we first need to calculate the common difference. We are given that the third term (a3) is -1592 and the fifth term (a5) is -3192. In an arithmetic sequence, any term can be found using the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
Since the sequence is arithmetic, the difference between consecutive terms is constant. To find the common difference (d), we use the formula d = an - an-1. So, we have:
d = a5 - a3 = (-3192) - (-1592) = -1600. However, this is the difference covering two terms, so the common difference for one term is:
d = -1600/2 = -800.
Next, we find the first term (a1) using the formula with a3:
a1 = a3 - 2d = -1592 - (2 * -800) = -1592 + 1600 = 8.
Now, we can write the general formula for the nth term of the sequence:
an = a1 + (n - 1)d.
an = 8 + (n - 1)(-800).
This is the formula to determine the nth term of the given arithmetic sequence.