Final answer:
The nth term of the given sequence 2, -98, -198, -298, -398 is -98 - 100n.The nᵗʰ term of the sequence is found using the arithmetic sequence formula, and it turns out to be 102 - 100n.
Step-by-step explanation:
The given sequence is 2, -98, -198, -298, -398. To determine the nth term of this sequence, we can observe that each term is decreasing by 100 and starting with 2. This means that the common difference or change between each term is -100. We can use the formula for the nth term of an arithmetic sequence, which is:
an = a1 + (n - 1)d
Where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. In this case, a1 = 2 and d = -100.
Plugging these values into the formula, we get:
an = 2 + (n - 1)(-100)
To simplify further, we can distribute the -100:
an = 2 - 100n + 100
an = -98 - 100n
Therefore, the nth term of the given sequence is -98 - 100n.