To find the missing term in each geometric sequence, we need to identify the common ratio (r) between consecutive terms.
In the sequence 54, ___, 1944, we can find the common ratio by dividing any term by its preceding term:
r = 1944 / 54 = 36
Now, we can use the common ratio to find the missing term. Let's call it x:
54, 54 * r, 1944
54 * r = x
x = 54 * 36 = 1944
Therefore, the missing term in the sequence is 1944.
In the sequence 29, ___, 464, we can again find the common ratio:
r = 464 / 29 = 16
Using the common ratio, we can find the missing term:
29, 29 * r, 464
29 * r = x
x = 29 * 16 = 464
Thus, the missing term in the sequence is 464.
Therefore, for the given geometric sequences, the missing terms are 1944 and 464, respectively.