Final answer:
The nth term of the sequence -8, 292, 592, 892, 1192 is determined by the formula an = 300n - 308, where n represents the term's position in the sequence.
Step-by-step explanation:
To find the nth term of the sequence -8, 292, 592, 892, 1192, we should first recognize the pattern. The difference between consecutive terms is constant, which indicates this is an arithmetic sequence. This constant difference is 300 (292 - (-8) = 300, 592 - 292 = 300, etc.).
We can express the nth term of an arithmetic sequence using the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and d is the common difference between the terms.
For our sequence:
a1 = -8 (the first term)
d = 300 (the common difference)
Therefore, the nth term, an, is:
an = -8 + (n - 1)×300
Expanding this, we get:
an = -8 + 300n - 300
an = 300n - 308
This is the formula for the nth term of the given sequence.