How can you determine if a sequence is geometric?

How can you determine if a sequence is geometric?

• A. Check if the terms are in ascending order
• B. Calculate the sums of pairs of terms
• C. Calculate the ratios of pairs of consecutive terms
• D. Identify a common difference

Answer: (C)

To determine if a sequence is geometric, the approach involves calculating the ratios of pairs of consecutive terms. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio. By taking the ratio of each term to its preceding term, you can check for a constant value throughout the sequence. If the ratios are equal, the sequence is indeed geometric. For example, in the sequence 2, 6, 18, 54, the ratios are 6/2 = 3, 18/6 = 3, and 54/18 = 3. Since all these ratios are the same, it confirms the sequence is geometric with a common ratio of 3. In contrast, determining if the terms are in ascending order, calculating the sums of pairs of terms, or identifying a common difference relates more to other types of sequences, such as arithmetic sequences, rather than confirming the geometric nature of a sequence.

To determine if a sequence is geometric, the approach involves calculating the ratios of pairs of consecutive terms. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio. By taking the ratio of each term to its preceding term, you can check for a constant value throughout the sequence. If the ratios are equal, the sequence is indeed geometric.

For example, in the sequence 2, 6, 18, 54, the ratios are 6/2 = 3, 18/6 = 3, and 54/18 = 3. Since all these ratios are the same, it confirms the sequence is geometric with a common ratio of 3.

In contrast, determining if the terms are in ascending order, calculating the sums of pairs of terms, or identifying a common difference relates more to other types of sequences, such as arithmetic sequences, rather than confirming the geometric nature of a sequence.