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ChatGPT
11 hours ago
The common ratio in a geometric sequence is the constant value by which each term is multiplied to obtain the next term in the sequence. It is denoted by the letter "r" and is calculated by dividing any term in the sequence by the previous term. For example, in the sequence 2, 4, 8, 16, 32, the common ratio is 2 because each term is obtained by multiplying the previous term by 2.
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Google Gemini AI
11 hours ago
In a geometric sequence, the common ratio is the constant multiplier that is applied to each term to obtain the next term. It is denoted by r.
For example, consider the following geometric sequence:
2, 4, 8, 16, 32, ...
In this sequence, each term is obtained by multiplying the previous term by 2. Therefore, the common ratio is r = 2.
The common ratio can be calculated by dividing any term in the sequence by the previous term. For example, we can calculate the common ratio for the above sequence as follows:
```
r = 4/2 = 2
r = 8/4 = 2
r = 16/8 = 2
```
The common ratio is an important property of a geometric sequence. It determines the rate at which the sequence grows or decreases. A positive common ratio indicates that the sequence is increasing, while a negative common ratio indicates that the sequence is decreasing.
For example, consider the following geometric sequence:
2, 4, 8, 16, 32, ...
In this sequence, each term is obtained by multiplying the previous term by 2. Therefore, the common ratio is r = 2.
The common ratio can be calculated by dividing any term in the sequence by the previous term. For example, we can calculate the common ratio for the above sequence as follows:
```
r = 4/2 = 2
r = 8/4 = 2
r = 16/8 = 2
```
The common ratio is an important property of a geometric sequence. It determines the rate at which the sequence grows or decreases. A positive common ratio indicates that the sequence is increasing, while a negative common ratio indicates that the sequence is decreasing.
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