Final answer:
The nᵗʰ term of the sequence -9, 891, 1791, 2691, 3591 is found using the arithmetic sequence formula Tn = a + (n - 1)d. The common difference (d) is 900, and the first term (a) is -9. The formula for the nᵗʰ term is Tn = 900n - 909.
Step-by-step explanation:
The sequence -9, 891, 1791, 2691, 3591 seems to be increasing by a common difference each time, which is a characteristic of an arithmetic sequence. To find the nᵗʰ term of an arithmetic sequence, we use the formula Tn = a + (n - 1)d, where Tn is the nᵗʰ term, a is the first term, n is the term number, and d is the common difference between the terms.
By examining the sequence, we determine the common difference d is 900 (891 - (-9) = 900). The first term a is -9. Plugging these values into the formula, we get Tn = -9 + (n - 1)(900). Simplifying, we find that the nᵗʰ term is equal to Tn = 900n - 909.
The given sequence -9, 891, 1791, 2691, 3591 follows a pattern where the nth term can be represented as n^2. To understand this pattern, we can consider the difference between consecutive terms. The difference between the first two terms is 891 - (-9) = 900, which is equal to 30^2. Similarly, the difference between the second and third terms is 1791 - 891 = 900, which is also equal to 30^2. This pattern continues for the remaining terms as well.
Therefore, the nth term of the sequence can be given by n^2. For example, the 6th term would be 6^2 = 36, and the 7th term would be 7^2 = 49.