Determine weather each sequence is arithmetic,geometric,or neither3,3/2,1,3/4,...
A. arithmetic,the common difference is -1.5
B. Arithmetic,the common difference is -0.5
C. Geometric,the common ratio is -1.5/1
D. Neither, there is no common difference or radio
Determine weather each sequence is arithmetic,geometric,or neither 7,13,19,25,..
Well, let's see. The sequence is 3, 3/2, 1, 3/4,... To determine whether it is arithmetic or geometric, we need to look for a common difference or a common ratio.
If we subtract the previous term from the next term, we can see that we get -1/2, -1/2, -1/4,... Aha! That means there is a constant difference of -1/2. So, it is an arithmetic sequence.
Therefore, option B is correct. It is arithmetic, with a common difference of -0.5.
But hey, life is full of surprises, so always be ready for unexpected patterns, like a clown appearing out of nowhere! *honk honk*
To determine whether the given sequence is arithmetic, geometric, or neither, we need to analyze the pattern and determine if there is a common difference or a common ratio.
Looking at the sequence: 3, 3/2, 1, 3/4, ...
We can see that the difference between each consecutive term is not constant, and therefore, there is no common difference. Thus, we can eliminate options A and B, which suggest that the sequence is arithmetic with common differences of -1.5 and -0.5.
Next, let's check if there is a common ratio for this sequence.
We can see that each term is obtained by dividing the previous term by 2. In other words, we have:
3/2 ÷ 3 = 1/2
1 ÷ (3/2) = 2/3
(3/4) ÷ (1/2) = 3/2
Therefore, the sequence does have a common ratio of 1/2.
Since there is a common ratio, we can conclude that the given sequence is geometric.
However, option C suggests that the common ratio is -1.5/1, which is incorrect. Thus, we can eliminate option C.
Therefore, the correct answer is D. Neither, since the sequence is geometric with a common ratio of 1/2.
To determine whether a sequence is arithmetic, geometric, or neither, we need to check if there is a constant difference or ratio between consecutive terms.
Let's analyze the given sequence: 3, 3/2, 1, 3/4, ...
To find the common difference, we subtract each term from the previous one:
3 - 3/2 = 3/2 - 1 = 1 - 3/4 = ...
The differences are not constant as they vary between 3/2, -1/2, -1/4, etc. Since there is no constant difference, we can conclude that the sequence is not arithmetic.
To find the common ratio, we divide each term by the previous one:
(3/2) / 3 = 1/2, 1 / (3/2) = 2/3, (3/4) / 1 = 3/4, ...
The ratios are not constant as they vary between 1/2, 2/3, 3/4, etc. Since there is no constant ratio, we can conclude that the sequence is not geometric.
Therefore, the correct answer is:
D. Neither, there is no common difference or ratio.