Final answer:
The sequence 9, -591, -1191, -1791, -2391 has a common difference of -600. The nᵗʰ term can be found using the arithmetic sequence formula, which results in the nᵗʰ term being 609 - 600n for this particular sequence.
Step-by-step explanation:
The given sequence is 9, -591, -1191, -1791, -2391. By examining the sequence, we can find the pattern by which each term is found. We will subtract each term from its predecessor to find the common difference.
- -591 - 9 = -600
- -1191 - (-591) = -600
- -1791 - (-1191) = -600
- -2391 - (-1791) = -600
We can see that the common difference is -600. To find the nᵗʰ term, 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.
For this sequence:
Substitute the values into the equation:
an = 9 + (n - 1)(-600)
an = 9 - 600n + 600
an = 609 - 600n
Therefore, the nᵗʰ term of the sequence is 609 - 600n.