Final answer:
The nth term of the sequence 1, -99, -199, -299, -399 is given by the formula 101 - 100n, which is derived from identifying the sequence as an arithmetic sequence with a common difference of -100.
Step-by-step explanation:
To determine the nth term of the given sequence 1, -99, -199, -299, -399, we need to find the pattern of the sequence and derive a formula that can calculate any term in the sequence based on its position, n.
Looking at the sequence, the difference between successive terms is -100:
This pattern indicates that the sequence is arithmetic with a common difference of -100. The arithmetic sequence formula is given by:
an = a1 + (n - 1)d
Where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.
Using the formula, let's plug in the values:
Now, the nth term is:
an = 1 + (n - 1)(-100)
= 1 - 100n + 100
= 101 - 100n
Therefore, the nth term of the sequence is 101 - 100n.