find the common ratio of each sequence:
1. 8,20,50,125......?
2. 0.48,0.9,1.8,3.6.....?
The ratio of the first sequence is 2.5 so the recursive formula is going to be an= 2.5(an-1)
-3,-9,-27
To find the common ratio of a sequence, you need to divide any term by its preceding term. Let's find the common ratio for each sequence:
1. For the sequence 8, 20, 50, 125, we divide each term by its preceding term:
- The common ratio between 20 and 8 is 20 / 8 = 2.5
- The common ratio between 50 and 20 is 50 / 20 = 2.5
- The common ratio between 125 and 50 is 125 / 50 = 2.5
Hence, the common ratio for this sequence is 2.5.
2. For the sequence 0.48, 0.9, 1.8, 3.6, we divide each term by its preceding term:
- The common ratio between 0.9 and 0.48 is 0.9 / 0.48 ≈ 1.875
- The common ratio between 1.8 and 0.9 is 1.8 / 0.9 = 2
- The common ratio between 3.6 and 1.8 is 3.6 / 1.8 = 2
As you can see, the common ratio changes from 1.875 to 2 between the second and third term. This means the sequence is not geometric, and there is no constant common ratio.
To summarize:
1. The common ratio for the first sequence is 2.5.
2. The second sequence does not have a common ratio since it is not geometric.
to find the common ration, divide any term by the term before it.
e.g. r = 50/20 = ....
let me know what you come up with for both of your questions.