The common ratio of the sequence 2, 6, 18, 54 can be found by dividing any term in the sequence by the previous term.
Starting from the first two terms:
- Common ratio = 6 ÷ 2 = 3
Now, let’s verify using the next terms:
- Common ratio = 18 ÷ 6 = 3
- Common ratio = 54 ÷ 18 = 3
As we can see, the common ratio is consistently 3 throughout the sequence. This indicates that each term is multiplied by 3 to get the next term. Thus, the common ratio for the sequence is 3.