The sequence you provided is 2, 6, 18, 54. To determine the common ratio, we need to look at how each term relates to the one before it.
The common ratio (r) of a geometric sequence is found by dividing any term by the preceding term. Let’s calculate it:
- For the first two terms:
- r = 6 / 2 = 3
- For the second and third terms:
- r = 18 / 6 = 3
- For the third and fourth terms:
- r = 54 / 18 = 3
As we can see from these calculations, the common ratio is consistent throughout the sequence:
Common Ratio (r) = 3
This means that each term in the sequence is obtained by multiplying the previous term by 3. This pattern is a defining characteristic of a geometric sequence. In this case, since the common ratio is greater than 1, it indicates that the sequence is increasing.
In summary, the common ratio of the sequence 2, 6, 18, 54 is 3.