To determine the common ratio of a geometric sequence, we can divide any term by the previous term. In this sequence, the terms are: 625, 125, 25, 5, and 1. Let’s calculate the common ratio using the first two terms:
Common ratio (r) = second term / first term = 125 / 625
Calculating that gives us:
r = 125 / 625 = 0.2
Now, let’s confirm this by looking at the other consecutive pairs of terms:
- r = third term / second term = 25 / 125 = 0.2
- r = fourth term / third term = 5 / 25 = 0.2
- r = fifth term / fourth term = 1 / 5 = 0.2
As you can see, in every case, the value of the common ratio is consistently 0.2. Therefore, we can conclude that the common ratio of the geometric sequence 625, 125, 25, 5, 1 is: