Final answer:
The nth term of the sequence 7, -13, -33, -53, -73 is found by identifying it as an arithmetic sequence with a common difference of -20. Using the formula for the nth term of an arithmetic sequence, the nth term is 27 - 20n.
Step-by-step explanation:
To determine the nth term of the given sequence 7, -13, -33, -53, -73, we need to find a pattern or rule that describes how the sequence progresses. Examining the differences between terms, we note that the sequence decreases by 20 each time:
- -13 - 7 = -20
- -33 - (-13) = -20
- -53 - (-33) = -20
- -73 - (-53) = -20
This is an arithmetic sequence with a common difference of -20. The nth term of an arithmetic sequence can be found using the formula an = a1 + (n - 1)d, where a1 is the first term and d is the common difference.
Thus, the nth term is:
an = 7 + (n - 1)(-20)
an = 7 - 20n + 20
an = 27 - 20n