Final answer:
The nth term of the sequence 1, 201, 401, 601, 801 is determined to be 200n - 199 by recognizing it as an arithmetic sequence with a common difference of 200 and applying the formula for the nth term of an arithmetic sequence.
Step-by-step explanation:
To find the nth term of the given sequence 1, 201, 401, 601, 801, we need to determine the pattern of the sequence. Upon examining the sequence, we observe that each term is increasing by 200. In other words, the sequence is an arithmetic sequence with a common difference (d) of 200. The general formula for the nth term of an arithmetic sequence is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and n is the term number.
For this sequence:
- The first term, a1, is 1.
- The common difference, d, is 200.
Substitute these values into the formula:
an = 1 + (n - 1)(200)
an = 1 + 200n - 200
an = 200n - 199
Therefore, the nth term of the sequence is 200n - 199.