Final answer:
The nth term of the sequence is an arithmetic sequence with a common difference of -900. The formula for the nth term is an = -900n + 906.
Step-by-step explanation:
To determine the nth term of the given sequence 6, -894, -1794, -2694, -3594, we need to find a pattern that relates each term to its position (n) in the sequence. Let's examine the differences between consecutive terms:
Difference between 1st and 2nd term: -894 - 6 = -900
Difference between 2nd and 3rd term: -1794 - (-894) = -900
Difference between 3rd and 4th term: -2694 - (-1794) = -900
Difference between 4th and 5th term: -3594 - (-2694) = -900
The constant difference of -900 suggests that the sequence is arithmetic. Therefore, the nth term (an) can be calculated using the formula:
an = a1 + (n - 1)d where a1 is the first term and d is the common difference.
For this sequence:
a1 = 6
d = -900
The nth term is therefore:
an = 6 + (n - 1)(-900) = 6 - 900n + 900 = -900n + 906.