Final answer:
The missing term in the geometric sequence 1/4, 1/2, ?, 1, 5/4 is 1, as the sequence has a common ratio of 2. This is evident by multiplying each term by 2 to get the next term, and our answer is confirmed as reasonable when continuing the pattern.
Step-by-step explanation:
To determine the unknown term in the sequence 1/4, 1/2, ?, 1, 5/4, we need to first identify if the sequence is arithmetic or geometric. An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio. By examining the given terms, we see that multiplying 1/4 by 2 gives us 1/2, and multiplying 1 by 1.25 gives us 5/4. Therefore, it appears to be a geometric sequence with a common ratio.
Now, we identify the knowns: the terms 1/4, 1/2, and 1. To find the missing term, we need to multiply the second term, 1/2, by the common ratio. Since 1/4 times 2 equals 1/2, the common ratio is 2. So multiplying 1/2 by 2 gives us the missing term, which is 1 (1/2 * 2 = 1).
This confirms that the sequence is indeed geometric, and the unknown term is 1. To check that the answer is reasonable, we can continue the pattern to ensure that the next term is 5/4 when multiplying by the common ratio, which it is (1 * 1.25 = 5/4).