Final answer:
The explicit formula for the nth term of the sequence 1, -9, -19, ... is an = -10n + 11. This formula is based on the first term being 1 and the common difference in the sequence being -10.
Step-by-step explanation:
To find the explicit formula for the n terms of the sequence 1, -9, -19, ..., we can observe the pattern in the differences between consecutive terms. The difference between the first and second term is -10, and the difference continues as such for subsequent terms. Since the first term is 1, we can derive the formula based on the common difference of -10.
Starting with the first term a1 = 1, the second term would be a1 + (-10) = -9, and the third term would be a1 + 2(-10) = -19, and so on. Therefore, for the nth term, the formula would be:
an = 1 + (n - 1)(-10) = 1 - 10n + 10 = -10n + 11.
Comparing with the provided options, the correct explicit formula is:
A) an = -10n + 11