is the sequence 2,3,5,8,12 geometric? please explain why
No, it isn't. In a geometric sequence, there is a fixed number multiplied by a term to get the next term. This is an example of geometric sequence:
3, 6, 12, 24, 48, ...
Here, we can see that each term is multiplied by two to get the next term.
3*2 = 6 ; 6*2 = 12, and so on.
Thus the ratio of two consecutive terms must be equal:
6/3 = 12/6 ; 12/6 = 24/12
In the problem given above,
3/2 ≠ 5/3 ; 8/5 ≠ 12/8
Therefore, it's not a geometric sequence.
Hope this helps~ `u`
Well, this sequence is geometrically challenging. Let's see... If you divide 3 by 2, you get 1.5. Then if you divide 5 by 3, you get approximately 1.6667. But if you divide 8 by 5, you get 1.6. Now that's confusing, isn't it? And if you divide 12 by 8, you get 1.5 again. So, as you can see, this sequence is not really following a consistent geometric pattern. It's as unpredictable as a clown slipping on a banana peel!
To determine whether a sequence is geometric, we need to check if there is a common ratio between consecutive terms. In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio.
Let's examine the given sequence: 2, 3, 5, 8, 12.
To find the common ratio, we divide each term by its preceding term:
3 / 2 = 1.5
5 / 3 = 1.67 (rounded to two decimal places)
8 / 5 = 1.6
12 / 8 = 1.5
Based on these calculations, we can see that the sequence does not have a constant common ratio. The ratios between successive terms are not the same, indicating that the sequence is not geometric.
Therefore, the sequence 2, 3, 5, 8, 12 is not geometric.
To determine if a sequence is geometric, we need to check if there is a common ratio between consecutive terms. In a geometric sequence, each term is found by multiplying the previous term by the same constant factor.
To determine if the sequence 2, 3, 5, 8, 12 is geometric, let's calculate the ratios between consecutive terms:
3/2 = 1.5
5/3 = 1.667
8/5 = 1.6
12/8 = 1.5
As we can see, the ratios are not constant. In a geometric sequence, the ratios between consecutive terms should be constant. In this case, the ratios vary between 1.5 and 1.667, which means that the sequence 2, 3, 5, 8, 12 is not geometric.
Thus, we have determined that the given sequence is not geometric because the ratios between consecutive terms are not constant.