Final answer:
To fill in the gaps in the geometric sequence, we have determined the common ratio by dividing subsequent terms (25/1 = 25) and then used the ratio to find the missing numbers. These missing numbers are 5 and 625, making the answer A) 5, 625.
Step-by-step explanation:
The question provided is asking us to fill in the missing numbers in a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. Given the terms 1, ..., 25, 125, ..., we can find the common ratio by dividing 25 by 1, which is 25. Using this ratio, we can multiply 1 by 25 to find the second term, and 125 by 25 to find the sixth term. Therefore, the terms that complete the sequence are 5 and 625.
The sequence becomes: 1, 5, 25, 125, 625.
The correct answer to the student's question is A) 5, 625.