Final answer:
The common ratio of the geometric sequence 2/9, 2/3, 2, 6 is 3.
Step-by-step explanation:
The common ratio of the geometric sequence 2/9, 2/3, 2, 6 can be found by dividing each term by the previous term. Let's divide the second term by the first term:
2/3 ÷ 2/9 = 2/3 × 9/2 = 18/6 = 3
Similarly, let's divide the third term by the second term:
2 ÷ 2/3 = 2 × 3/2 = 6/2 = 3
Finally, let's divide the fourth term by the third term:
6 ÷ 2 = 3
As we can see, the common ratio of the given geometric sequence is 3.