The common ratio of a geometric sequence can be found by dividing any term by its preceding term. In the given sequence, we have:
1. The first term (a1) is 125.
2. The second term (a2) is 25.
3. The third term (a3) is 5.
4. The fourth term (a4) is 1.
To find the common ratio (r), we can use the formula:
r = a2 / a1
Calculating this, we have:
r = 25 / 125 = 1 / 5
We can confirm the common ratio by checking the ratio for the other pairs of terms:
r = a3 / a2 = 5 / 25 = 1 / 5
r = a4 / a3 = 1 / 5 = 1 / 5
Since we get the same ratio (1/5) for each pair of terms, we can conclude that the common ratio of the sequence is:
1/5