Final answer:
Among the provided sequences, the first (2, 3, 4.5, 6.75, …) and the last (8, 4, 2, 1, …) are geometric series because each term is obtained by multiplying by a constant ratio.
Step-by-step explanation:
To identify which sequences represent a geometric series, we must determine if each term after the first is obtained by multiplying the previous term by the same nonzero number (common ratio). Let's analyze the sequences provided:
2, 3, 4.5, 6.75, …: This is a geometric series because each term is obtained by multiplying the previous term by 1.5 (common ratio).
2, 2.5, 3, 3.5, …: This is not a geometric series because the difference between terms is being added, not multiplied.
6, 7, 9, 12, …: This is not a geometric series as there is no common ratio.
4, 8, 16, 20, …: This is not a geometric series because the ratio between terms is not consistent.
8, 4, 2, 1, …: This is a geometric series because each term is obtained by multiplying the previous term by 0.5 (common ratio).
Hence, the sequences that represent geometric series are the first (2, 3, 4.5, 6.75, …) and the last (8, 4, 2, 1, …).