Which of the following patterns is an arithmetic sequence? You may choose more than 1 answer.(2 points)
Responses
2,4,8,16...
2,4,8,16...
-9,-17,-25,-33...
-9,-17,-25,-33...
12,13,16,0...
2,20,200,2000...
The following patterns are arithmetic sequences:
2,4,8,16...
-9,-17,-25,-33...
2,20,200,2000...
These patterns have a common difference between consecutive terms which is consistent throughout the sequence.
The correct answer is:
2,4,8,16...
-9,-17,-25,-33...
These two patterns are arithmetic sequences. In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. In the first sequence, the difference between each term is 2, and in the second sequence, the difference is -8.
To determine which of the following patterns is an arithmetic sequence, we need to check if the difference between consecutive terms is constant.
Let's examine each pattern:
1. 2, 4, 8, 16...
To find the difference between consecutive terms, we subtract each term from its preceding term:
4 - 2 = 2
8 - 4 = 4
16 - 8 = 8
The differences (2, 4, 8) are not constant, so this pattern is not an arithmetic sequence.
2. -9, -17, -25, -33...
Calculating the differences between consecutive terms:
-17 - (-9) = -17 + 9 = -8
-25 - (-17) = -25 + 17 = -8
-33 - (-25) = -33 + 25 = -8
The differences (-8, -8) are constant, so this pattern is an arithmetic sequence.
3. 12, 13, 16, 0...
Finding the differences between consecutive terms:
13 - 12 = 1
16 - 13 = 3
0 - 16 = -16
The differences (1, 3, -16) are not constant; therefore, this pattern is not an arithmetic sequence.
4. 2, 20, 200, 2000...
Computing the differences between consecutive terms:
20 - 2 = 18
200 - 20 = 180
2000 - 200 = 1800
The differences (18, 180, 1800) are not constant, so this pattern is not an arithmetic sequence.
Based on our analysis, the only pattern that represents an arithmetic sequence is:
-9, -17, -25, -33...