identify the sequence as arithmetic, geometric, or neither 3, 4.5,6,7.5,...
arithmetic, adding 1.5 each interval
To determine if the given sequence is arithmetic, geometric, or neither, we need to identify the pattern between consecutive terms.
Let's look at the differences between consecutive terms:
4.5 - 3 = 1.5
6 - 4.5 = 1.5
7.5 - 6 = 1.5
The differences between consecutive terms are constant and equal to 1.5. Thus, the sequence has a common difference of 1.5, which means it is an arithmetic sequence.
Therefore, the given sequence 3, 4.5, 6, 7.5,... is an arithmetic sequence.
To identify whether a sequence is arithmetic, geometric, or neither, we need to look at the pattern of the numbers.
In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. For example: 1, 3, 5, 7, ...
In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. For example: 2, 4, 8, 16, ...
Let's analyze the given sequence: 3, 4.5, 6, 7.5, ...
To determine if it is an arithmetic sequence, we can check if there is a constant difference between consecutive terms. Let's calculate the differences:
4.5 - 3 = 1.5
6 - 4.5 = 1.5
7.5 - 6 = 1.5
As we can see, the difference between each term is 1.5, which is a constant. Therefore, the given sequence is an arithmetic sequence with a common difference of 1.5.
If you are not sure about the pattern by just looking at the given terms, you can calculate the differences between consecutive terms and check if they are the same. If they are, then it is an arithmetic sequence.
In conclusion, the sequence 3, 4.5, 6, 7.5, ... is an arithmetic sequence.