Final answer:
The sequence is a geometric sequence with a common ratio of 0.25. The explicit rule for the sequence is an = -1,171,875 × 0.25^(n-1), where an is the nth term of the sequence.
Step-by-step explanation:
Analyzing the given sequence {-1,171,875; -234,375; -46,875; -9,375, ...}, we can observe the pattern of each subsequent number being a division by a common ratio. Each term is ⅔ (or 0.25) times the term before it. This is a geometric sequence. To find the explicit rule, we will use the formula for a geometric sequence, which is an = a1 × r(n-1), where an is the nth term, a1 is the first term, and r is the common ratio. Since the first term a1 is -1,171,875 and the common ratio r is 0.25, we have the explicit rule: an = -1,171,875 × 0.25(n-1).