Answer:
3
Explanation:
To find the missing term in the geometric sequence 6, [?], 3/2, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
where a1 is the first term, r is the common ratio, and n is the term number.
We know that the first term is 6, and the third term is 3/2. So, we can write:
a1 = 6
an = 3/2
Using the formula above, we can solve for the common ratio:
an = a1 * r^(n-1)
3/2 = 6 * r^(3-1)
3/2 = 6r^2
r^2 = 1/4
r = 1/2 or r = -1/2
Since the common ratio is positive (the sequence is increasing), we can take r = 1/2. Now we can use the formula to find the missing term:
an = a1 * r^(n-1)
an = 6 * (1/2)^(n-1)
To find the missing term, we need to find the value of n. We know that the missing term is between 6 and 3/2, so it must be less than 6. We can try plugging in different values of n until we find the one that gives a term between 6 and 3/2:
n = 2: a2 = 6 * (1/2)^(2-1) = 3
n = 3: a3 = 6 * (1/2)^(3-1) = 1.5
Therefore, the missing term in the sequence is 3.