No, the sequence 1, 2, 4, 8 is not an arithmetic sequence.
Understanding Arithmetic Sequences
An arithmetic sequence is a sequence where the difference between consecutive terms remains constant. This constant difference is called the common difference. For example, in the sequence 2, 5, 8, 11, the common difference is 3 (5-2 = 3, 8-5 = 3, 11-8 = 3).
Analyzing the Sequence 1, 2, 4, 8
Let's examine the differences between consecutive terms in the given sequence:
- 2 - 1 = 1
- 4 - 2 = 2
- 8 - 4 = 4
Since the differences are not constant, the sequence does not have a common difference. Therefore, it's not an arithmetic sequence.
Identifying the Type of Sequence
The provided references clearly state that the sequence 1, 2, 4, 8 is a geometric sequence. This is because there's a common ratio between consecutive terms. In this case, each term is obtained by multiplying the previous term by 2.
- 1 x 2 = 2
- 2 x 2 = 4
- 4 x 2 = 8
This consistent multiplication by 2 defines the sequence as geometric, not arithmetic.
