The common ratio in the geometric sequence 2, 6, 18, 54 is 3.
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 in the given sequence, you can divide any term by its preceding term. Let's illustrate this with the provided sequence:
Example:
Given the sequence: 2, 6, 18, 54
- To find the common ratio, divide the second term by the first term: 6 / 2 = 3
- Verify by dividing the third term by the second term: 18 / 6 = 3
- Confirm by dividing the fourth term by the third term: 54 / 18 = 3
Since the ratio is consistently 3, the common ratio for this geometric sequence is 3.
According to the reference, "in the geometric sequence 2, 6, 18, 54, 162, …, the ratio is always 3. This is called the common ratio."
| Term | Value |
|---|---|
| First Term | 2 |
| Second Term | 6 |
| Third Term | 18 |
| Fourth Term | 54 |
As you can see, each term is a product of the previous term multiplied by 3.
