Which of the following are examples of an arithmetic sequence?
Responses
1, −3, −7, −11, −15, −19
1, −3, −7, −11, −15, −19
5, 9, 13, 17, 19, 20
5, 9, 13, 17, 19, 20
10, 8, 6, 4, 2, 0
10, 8, 6, 4, 2, 0
2, 4, 8, 16, 32, 64
2, 4, 8, 16, 32, 64
To determine which of the following sequences are examples of an arithmetic sequence, we need to check if the difference between consecutive terms is constant.
1. In the first sequence, the difference between consecutive terms is -3 - 1 = -4, -7 - (-3) = -4, and so on. Therefore, the first sequence is an arithmetic sequence with a common difference of -4.
2. In the second sequence, the difference between consecutive terms is 9 - 5 = 4, 13 - 9 = 4, and so on. Therefore, the second sequence is an arithmetic sequence with a common difference of 4.
3. In the third sequence, the difference between consecutive terms is 8 - 10 = -2, 6 - 8 = -2, and so on. Therefore, the third sequence is not an arithmetic sequence since the common difference is not consistent.
4. In the fourth sequence, the difference between consecutive terms is 4 - 2 = 2, 8 - 4 = 4, and so on. Therefore, the fourth sequence is not an arithmetic sequence since the common difference is not consistent.
Therefore, the examples of arithmetic sequences are:
1. 1, -3, -7, -11, -15, -19
2. 5, 9, 13, 17, 19, 20