Which of the following patterns is an arithmetic sequence? You may choose more than 1 answer.(2 points) Responses -9,-17,-25,-33... -9,-17,-25,-33... 2,4,8,16... 2,4,8,16... 2,20,200,2000... 2,20,200,2000... 1/2,1/3,1/6,0...
The following patterns are arithmetic sequences:
-9, -17, -25, -33...
2, 4, 8, 16...
To determine which of the given patterns is an arithmetic sequence, we need to check if the terms of the sequence have a common difference. This can be done by subtracting each term from the next term in the sequence.
Let's go through each option:
1) -9, -17, -25, -33...
The common difference between each term is -8. Therefore, this pattern is an arithmetic sequence.
2) 2, 4, 8, 16...
The terms in this pattern are doubling each time. The common difference between each term is not the same, so this pattern is not an arithmetic sequence.
3) 2, 20, 200, 2000...
The terms in this pattern are increasing by multiplying by 10 each time. The common difference between each term is not the same, so this pattern is not an arithmetic sequence.
4) 1/2, 1/3, 1/6, 0...
The terms in this pattern are decreasing by dividing by 2 each time. The common difference between each term is not the same, so this pattern is not an arithmetic sequence.
Based on the analysis above, only option 1) -9, -17, -25, -33... is an arithmetic sequence.
The arithmetic sequences among the given patterns are:
1) -9, -17, -25, -33...
2) 2, 4, 8, 16...
Both of these patterns follow the arithmetic sequence formula, where each term is obtained by adding or subtracting a constant difference.