Which of the following patterns is an arithmetic sequence? You may choose more than 1 answer.(2 points)Responses2,4,8,16...2,4,8,16...2,20,200,2000...2,20,200,2000...-9,-17,-25,-33...-9,-17,-25,-33...12,13,16,0...
The following patterns are arithmetic sequences:
1) 2,4,8,16...
2) -9,-17,-25,-33...
The arithmetic sequences are:
1) 2, 4, 8, 16...
2) -9, -17, -25, -33...
Both of these patterns follow the common difference of adding a constant value each time to the previous term.
To identify an arithmetic sequence, we need to determine if there is a common difference between consecutive terms.
In the given options:
1) 2, 4, 8, 16... does have a common difference of 4.
2) 2, 20, 200, 2000... does not have a constant common difference between consecutive terms.
3) -9, -17, -25, -33... does have a common difference of -8.
4) 12, 13, 16, 0... does not have a constant common difference between consecutive terms.
Therefore, the patterns that represent an arithmetic sequence are:
1) 2, 4, 8, 16...
3) -9, -17, -25, -33...
Arrange the following from least to greatest common difference. (least on the bottom and highest on top)
To arrange the patterns from least to greatest common difference, we need to determine the value of the common difference for each pattern.
The patterns and their common differences are as follows:
1) 2, 4, 8, 16... (common difference = 4)
2) 2, 20, 200, 2000... (no constant common difference)
3) -9, -17, -25, -33... (common difference = -8)
4) 12, 13, 16, 0... (no constant common difference)
Arranging them from least to greatest common difference, we have:
-9, -17, -25, -33... (common difference = -8)
2, 4, 8, 16... (common difference = 4)
Therefore, the arrangement from least to greatest common difference is:
-9, -17, -25, -33...
2, 4, 8, 16...