To find the common ratio of a geometric sequence, you can divide any term by the previous term. In this case, we can calculate the common ratio using the first two terms of the sequence.
The first term is 625 and the second term is 125. We calculate the common ratio (r) as follows:
r = second term / first term = 125 / 625 = 1/5
Now, let’s verify this ratio with the other terms in the sequence:
- Third term (25) = Second term (125) × r = 125 × (1/5) = 25
- Fourth term (5) = Third term (25) × r = 25 × (1/5) = 5
- Fifth term (1) = Fourth term (5) × r = 5 × (1/5) = 1
Since the common ratio is consistent throughout the sequence, we can conclude that:
The common ratio of the geometric sequence is 1/5.