Final answer:
To find the missing geometric means of the sequence 9, _, _, 8/3, calculate the common ratio by equating the first term (9) to the fourth term (8/3) raised to the power of 3.
Step-by-step explanation:
To find the missing geometric means for the geometric sequence 9, _, _, 8/3, we need to determine the common ratio (r) of the sequence. Since we have terms a (first term), ar, ar2, and ar3 (fourth term) in a geometric sequence, and we know a = 9 and ar3 = 8/3, we can find r as follows:
ar3 = 8/3
9r3 = 8/3
r3 = (8/3) / 9
r3 = 8/27
r = (8/27)1/3
r = 2/3
Now that we have the common ratio, we can find the missing terms:
Second term: 9 * (2/3) = 6
Third term: 6 * (2/3) = 4
Therefore, the complete geometric sequence is 9, 6, 4, 8/3.