Final answer:
The common ratio in the geometric sequence 7, ?, ?, 875 is found by dividing the last term by the first term and then taking the cube root, resulting in a common ratio of approximately 5.
Step-by-step explanation:
To find the common ratio in a geometric sequence, we use the formula that relates consecutive terms by a constant multiplier. In this case, we have the sequence 7, ?, ?, 875. The common ratio (geometric mean) can be found by taking any term and dividing it by the previous term. In a situation where we have two unknown middle terms, as we can see from this sequence, it's possible to find the common ratio by taking the fourth term and dividing it by the first term, then taking the fourth root since there are three intervals between the four terms.
So, the common ratio 'r' is calculated as follows: r^3 = 875/7. Simplifying this, we use a calculator to find that r is approximately 5. Therefore, the complete sequence is 7, 35, 175, 875.