To find the common ratio of the given sequence 125, 25, 5, 1, we first need to understand what a common ratio is. In a geometric sequence, the common ratio (r) is the factor by which we multiply each term to get the next term.
Let’s calculate the common ratio step-by-step:
- Divide the second term by the first term:
r = 25 / 125 = 0.2 - Now, divide the third term by the second term:
r = 5 / 25 = 0.2 - Lastly, divide the fourth term by the third term:
r = 1 / 5 = 0.2
As we can see, the common ratio is consistent across all pairs of consecutive terms:
- From 125 to 25 = 0.2
- From 25 to 5 = 0.2
- From 5 to 1 = 0.2
Therefore, the common ratio of the sequence 125, 25, 5, 1 is 0.2.