The common ratio of the geometric sequence 81, 27, 9 is 1/3.
Understanding Geometric Sequences and Common Ratio
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant. This constant is called the common ratio. To find the common ratio, you can divide any term by the preceding term.
Calculating the Common Ratio
In the given sequence 81, 27, 9, we can calculate the common ratio as follows:
- Divide the second term (27) by the first term (81): 27 / 81 = 1/3
- Divide the third term (9) by the second term (27): 9 / 27 = 1/3
As we can see, the common ratio is consistently 1/3.
Examples of Geometric Sequences
Here are some examples of geometric sequences with their common ratios:
| Sequence | Common Ratio |
|---|---|
| 2, 4, 8, 16, ... | 2 |
| 100, 50, 25, ... | 1/2 |
| 1, -3, 9, -27, ... | -3 |
| S=1/3, 1/9, 1/27, 1/81,… | 1/3 |
In the reference material provided, the example S=1/3, 1/9, 1/27, 1/81,… also has a common ratio of 1/3 because 1/9 divided by 1/3 equals 1/3.
