What type of sequence is represented by the numbers 8, 24, 72, 144?

What type of sequence is represented by the numbers 8, 24, 72, 144?

• A. Geometric
• B. Arithmetic
• C. Neither
• D. Quadratic

Answer: (C)

To determine the type of sequence represented by the numbers 8, 24, 72, 144, we can analyze the relationships between consecutive terms. First, consider the ratios of consecutive terms to see if the sequence is geometric. A geometric sequence is characterized by each term being a constant multiple of the previous term. If we take the first two terms, 24 divided by 8 gives us a ratio of 3. The ratio of the third term (72) to the second term (24) is also 3, and similarly, 144 divided by 72 is also 2. Therefore, the ratio is not constant, which means the sequence is not geometric. Next, we can analyze the difference between consecutive terms. In an arithmetic sequence, the difference between each pair of consecutive terms is constant. The differences calculated here are: - 24 - 8 = 16 - 72 - 24 = 48 - 144 - 72 = 72 The differences, 16, 48, and 72, are not constant, indicating that the sequence is not arithmetic either. Lastly, we can also investigate whether the sequence could be quadratic. A quadratic sequence is typically represented by a second-degree

To determine the type of sequence represented by the numbers 8, 24, 72, 144, we can analyze the relationships between consecutive terms.

First, consider the ratios of consecutive terms to see if the sequence is geometric. A geometric sequence is characterized by each term being a constant multiple of the previous term. If we take the first two terms, 24 divided by 8 gives us a ratio of 3. The ratio of the third term (72) to the second term (24) is also 3, and similarly, 144 divided by 72 is also 2. Therefore, the ratio is not constant, which means the sequence is not geometric.

Next, we can analyze the difference between consecutive terms. In an arithmetic sequence, the difference between each pair of consecutive terms is constant. The differences calculated here are:

• 24 - 8 = 16

• 72 - 24 = 48

• 144 - 72 = 72

The differences, 16, 48, and 72, are not constant, indicating that the sequence is not arithmetic either.

Lastly, we can also investigate whether the sequence could be quadratic. A quadratic sequence is typically represented by a second-degree