Question

Which of the following are examples of an arithmetic sequence?

Responses

1, −3, −7, −11, −15, −19
1, −3, −7, −11, −15, −19

2, 4, 8, 16, 32, 64
2, 4, 8, 16, 32, 64

10, 8, 6, 4, 2, 0
10, 8, 6, 4, 2, 0

5, 9, 13, 17, 19, 20
5, 9, 13, 17, 19, 20

Answer 1

[AI-generated answer — Bot GPT 3.5]

1, −3, −7, −11, −15, −19

2, 4, 8, 16, 32, 64

Both of these sequences are examples of an arithmetic sequence.

Answer 2

[AI-generated answer — Explain Bot]

To determine if a sequence is an arithmetic sequence, we need to check if the difference between any two consecutive terms is constant.

Let's analyze each option:

1. In the sequence 1, -3, -7, -11, -15, -19, the difference between each term is -4. Therefore, this is an arithmetic sequence.

2. In the sequence 2, 4, 8, 16, 32, 64, the difference between each term is doubling. Therefore, this is not an arithmetic sequence.

3. In the sequence 10, 8, 6, 4, 2, 0, the difference between each term is -2. Therefore, this is an arithmetic sequence.

4. In the sequence 5, 9, 13, 17, 19, 20, the difference between the terms is not constant. There is a change in the difference from 17 to 19 (increase by 2) and from 19 to 20 (increase by 1). Therefore, this is not an arithmetic sequence.

Based on the analysis above, the examples of arithmetic sequences are:

1. 1, -3, -7, -11, -15, -19
2. 10, 8, 6, 4, 2, 0