identify the sequence 3888 , 216 , 12 , 2/3 , as arithmetic geometric neither of both
3888, 216, 12, 2/3. Right?
It´s a GP -> q = 1/18?
To determine the nature of the given sequence, we need to check if the differences between consecutive terms are constant.
Let's calculate the differences between the terms:
216 - 3888 = -3672
12 - 216 = -204
2/3 - 12 = -35 2/3
As you can see, the differences are not constant, which means the sequence is not arithmetic.
Now, let's check if the ratios between consecutive terms are constant:
216 / 3888 ≈ 0.0556
12 / 216 ≈ 0.0556
(2/3) / 12 ≈ 0.0556
The ratios are approximately equal, which indicates that the sequence is geometric.
Therefore, the given sequence 3888, 216, 12, 2/3 is a geometric sequence.
To identify whether the given sequence is arithmetic, geometric, or neither, we need to analyze the pattern and compare the terms in the sequence.
An arithmetic sequence is a sequence in which each term is obtained by adding a common difference to the previous term. This means that the difference between any two consecutive terms in an arithmetic sequence is constant.
A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a common ratio. This means that the ratio of any two consecutive terms in a geometric sequence is constant.
Let's examine the given sequence: 3888, 216, 12, 2/3
To determine if the sequence is arithmetic, we need to check if the difference between consecutive terms is constant. Let's calculate the differences:
216 - 3888 = -3672
12 - 216 = -204
2/3 - 12 = -11 2/3
As we can see, the differences are not constant. Therefore, the given sequence is not arithmetic.
To determine if the sequence is geometric, we need to check if the ratio between consecutive terms is constant. Let's calculate the ratios:
216 / 3888 = 1/18
12 / 216 = 1/18
2/3 / 12 = 1/18
As we can see, the ratios are constant and equal to 1/18. Therefore, the given sequence is geometric.
In conclusion, the given sequence is geometric. The common ratio between consecutive terms is 1/18.