which of the following are examples of an arithmetic sequence?
1,-3,-7,-11,-15,-19
5,9,13,17,19,20
10,8,6,4,2,0
2,4,8,16,32,64
To determine whether a sequence is an arithmetic sequence, we need to check if there is a common difference between consecutive terms.
Let's go through each option and check:
1. -3 - 1 = -4, -7 - (-3) = -4, -11 - (-7) = -4, -15 - (-11) = -4, -19 - (-15) = -4. This sequence has a common difference of -4, so it is an arithmetic sequence.
2. 9 - 5 = 4, 13 - 9 = 4, 17 - 13 = 4, 19 - 17 = 2, 20 - 19 = 1. This sequence does not have a constant common difference, so it is not an arithmetic sequence.
3. 8 - 10 = -2, 6 - 8 = -2, 4 - 6 = -2, 2 - 4 = -2, 0 - 2 = -2. This sequence has a common difference of -2, so it is an arithmetic sequence.
4. 4 - 2 = 2, 8 - 4 = 4, 16 - 8 = 8, 32 - 16 = 16, 64 - 32 = 32. This sequence does not have a constant common difference, so it is not an arithmetic sequence.
Therefore, the sequences that are arithmetic sequences are:
1. -3, -7, -11, -15, -19
3. 10, 8, 6, 4, 2, 0