Which of the following is an example of a geometric sequence?

A geometric sequence is defined by a common ratio between consecutive terms. In this case, the correct answer provides the sequence 2, 4, 8, 16. To verify that this is a geometric sequence, we can look at the ratio of each term to its previous term:

• The ratio of the second term (4) to the first term (2) is 4 ÷ 2 = 2.

• The ratio of the third term (8) to the second term (4) is 8 ÷ 4 = 2.

• The ratio of the fourth term (16) to the third term (8) is 16 ÷ 8 = 2.

Since the common ratio is consistently 2 across all terms, this confirms that the sequence is geometric.

In contrast, the other options represent different types of sequences. The first option is an arithmetic sequence, where each term increases by 1. The third and fourth options are also arithmetic sequences, where each term increases by 5 and 10, respectively. None of these sequences exhibit a constant ratio between the terms, which is what distinguishes geometric sequences from arithmetic ones.