Which of the following patterns is an arithmetic sequence?%C2%A0You may choose more than 1 answer.(2 points) Responses 2,20,200,2000... 12,13,16,0... -9,-17,-25,-33.... 2,4,8,16...
The arithmetic sequences in the given patterns are:
1) 2, 20, 200, 2000...
2) -9, -17, -25, -33...
3) 2, 4, 8, 16...
So the correct answer is:
1) 2, 20, 200, 2000...
3) 2, 4, 8, 16...
The arithmetic sequence among the given options is:
-9, -17, -25, -33...
To determine if a pattern is an arithmetic sequence, we need to check if there is a common difference between consecutive terms.
1. Responses: 2, 20, 200, 2000...
To find the common difference, we can calculate the ratio between consecutive terms:
Second term / First term = 20 / 2 = 10
Third term / Second term = 200 / 20 = 10
Fourth term / Third term = 2000 / 200 = 10
Since the ratio is constant (10), this pattern is an arithmetic sequence.
2. Responses: 12, 13, 16, 0...
To find the common difference, we can calculate the difference between consecutive terms:
Second term - First term = 13 - 12 = 1
Third term - Second term = 16 - 13 = 3
Fourth term - Third term = 0 - 16 = -16
Since the difference is not constant, this pattern is not an arithmetic sequence.
3. Responses: -9, -17, -25, -33...
To find the common difference, we can calculate the difference between consecutive terms:
Second term - First term = -17 - (-9) = -8
Third term - Second term = -25 - (-17) = -8
Fourth term - Third term = -33 - (-25) = -8
Since the difference is constant (-8), this pattern is an arithmetic sequence.
4. Responses: 2, 4, 8, 16...
To find the common difference, we can calculate the difference between consecutive terms:
Second term - First term = 4 - 2 = 2
Third term - Second term = 8 - 4 = 4
Fourth term - Third term = 16 - 8 = 8
Since the difference is not constant, this pattern is not an arithmetic sequence.
Based on our analysis, the arithmetic sequences are:
- Responses: 2, 20, 200, 2000...
- Responses: -9, -17, -25, -33...
Therefore, the correct answer is:
- Responses 2, 20, 200, 2000...
- Responses -9, -17, -25, -33...