Final answer:
The common difference of the sequence 1/4, 3/8, 1/2 is 1/8, which is found by ensuring the denominators are the same and subtracting consecutive terms.
Step-by-step explanation:
To find the common difference of the given sequence 1/4, 3/8, 1/2, ... we will look at the difference between consecutive terms. The second term (3/8) minus the first term (1/4) equals 3/8 - 1/4. To find this, we need to make the denominators the same.
The common denominator of 4 and 8 is 8, so we convert 1/4 to 2/8. Performing the subtraction, we get 3/8 - 2/8 = 1/8, which is the common difference. To confirm that 1/8 is indeed the common difference, check the difference between the third term (1/2) and the second term (3/8).
Convert 1/2 to 4/8 to get the same denominator and subtract: 4/8 - 3/8 = 1/8. Since the difference between each term is consistent, we can say that the common difference is 1/8.