The question asks for the ratio in the sequence 125, 25, 5. Based on the provided reference, which focuses on geometric progressions, the question is likely asking for the common ratio of the sequence assuming it is geometric. Let's analyze this.
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. To find the common ratio, we can divide any term by its preceding term.
Here's how we can find the ratio in the sequence 125, 25, 5:
- Divide the second term by the first term: 25 / 125 = 1/5
- Divide the third term by the second term: 5 / 25 = 1/5
As we can see, the ratio is consistent. Therefore, the common ratio of this sequence is indeed 1/5.
Calculation Summary
| Term | Value |
|---|---|
| First Term | 125 |
| Second Term | 25 |
| Third Term | 5 |
| Common Ratio (2nd term / 1st term) | 25/125 = 1/5 |
| Common Ratio (3rd term / 2nd term) | 5/25 = 1/5 |
The reference example gives a sequence -125, -25, -5, -1 ... where the common ratio is calculated in the same way and is 1/5. This further confirms the method used above to find the ratio and demonstrates that the ratio can also be found when the terms of the sequence are negative.
Therefore, the ratio of the sequence 125, 25, 5 is 1/5 assuming it is a geometric sequence.
