What is the next term in the provided geometric sequence that starts with 0.01?

What is the next term in the provided geometric sequence that starts with 0.01?

• A. 0.1
• B. 0.01
• C. 0.001
• D. 0.1.01

Answer: (C)

To determine the next term in a geometric sequence, it's essential to identify the common ratio that defines the relationship between the terms. In this case, the sequence begins with 0.01. To identify the common ratio, let's examine how the sequence grows. By observing the first term (0.01), we can infer the pattern of multiplication. For instance, if the next term in the sequence is 0.1, we can see that: 0.01 multiplied by 10 equals 0.1. This indicates that the common ratio is 10, meaning each subsequent term is obtained by multiplying the previous term by 10. Following this pattern, if we take 0.1 as the second term, the next term would be calculated as follows: 0.1 multiplied by 10 equals 1. Hence, if we continue this logic, calculating backward for the provided answer options, the term after 0.01 (the first term) would logically align with the provided options as: - The first term is 0.01. - The second term would indeed be 0.1, which is the next clear iteration in the sequence. Therefore, if you're moving downward through the powers of ten from 0.

To determine the next term in a geometric sequence, it's essential to identify the common ratio that defines the relationship between the terms. In this case, the sequence begins with 0.01.

To identify the common ratio, let's examine how the sequence grows. By observing the first term (0.01), we can infer the pattern of multiplication. For instance, if the next term in the sequence is 0.1, we can see that:

0.01 multiplied by 10 equals 0.1.

This indicates that the common ratio is 10, meaning each subsequent term is obtained by multiplying the previous term by 10.

Following this pattern, if we take 0.1 as the second term, the next term would be calculated as follows:

0.1 multiplied by 10 equals 1.

Hence, if we continue this logic, calculating backward for the provided answer options, the term after 0.01 (the first term) would logically align with the provided options as:

• The first term is 0.01.

• The second term would indeed be 0.1, which is the next clear iteration in the sequence.

Therefore, if you're moving downward through the powers of ten from 0.