Question
Select ALL of the following that are examples of an arithmetic sequence. (1 point)
Responses
3, 9, 27, 81, 243
3, 9, 27, 81, 243
You start at an elevation of 12,000 feet and climb down 1,000 feet per day.
You start at an elevation of 12,000 feet and climb down 1,000 feet per day.
1, 11, 21, 25, 31, 38
1, 11, 21, 25, 31, 38
20, 14, 8, 2, −4, −10
20, 14, 8, 2, −4, −10
You add $2 to a piggy bank and add triple the money you added the previous day for one month.
Responses
3, 9, 27, 81, 243
3, 9, 27, 81, 243
You start at an elevation of 12,000 feet and climb down 1,000 feet per day.
You start at an elevation of 12,000 feet and climb down 1,000 feet per day.
1, 11, 21, 25, 31, 38
1, 11, 21, 25, 31, 38
20, 14, 8, 2, −4, −10
20, 14, 8, 2, −4, −10
You add $2 to a piggy bank and add triple the money you added the previous day for one month.
Answers
GPT-4o mini
An arithmetic sequence is defined as a sequence of numbers in which the difference between consecutive terms is constant. Based on this definition, let's evaluate each option:
1. **3, 9, 27, 81, 243**: This sequence is not arithmetic. The differences are not constant (6, 18, 54, 162).
2. **You start at an elevation of 12,000 feet and climb down 1,000 feet per day**: This describes a linear pattern where you reduce your elevation by a constant amount (1,000 feet), which is an arithmetic sequence.
3. **1, 11, 21, 25, 31, 38**: This sequence is not arithmetic since the differences between consecutive terms are not consistent (10, 10, 4, 6, 7).
4. **20, 14, 8, 2, −4, −10**: This is an arithmetic sequence with a common difference of -6 (20-14, 14-8, 8-2, 2-(-4), -4-(-10) all equal -6).
5. **You add $2 to a piggy bank and add triple the money you added the previous day for one month**: This sequence grows in a multiplicative manner (tripling), making it non-arithmetic.
Based on this analysis, the examples of an arithmetic sequence are:
- **You start at an elevation of 12,000 feet and climb down 1,000 feet per day.**
- **20, 14, 8, 2, −4, −10.**
So, the correct selections are those two statements.
1. **3, 9, 27, 81, 243**: This sequence is not arithmetic. The differences are not constant (6, 18, 54, 162).
2. **You start at an elevation of 12,000 feet and climb down 1,000 feet per day**: This describes a linear pattern where you reduce your elevation by a constant amount (1,000 feet), which is an arithmetic sequence.
3. **1, 11, 21, 25, 31, 38**: This sequence is not arithmetic since the differences between consecutive terms are not consistent (10, 10, 4, 6, 7).
4. **20, 14, 8, 2, −4, −10**: This is an arithmetic sequence with a common difference of -6 (20-14, 14-8, 8-2, 2-(-4), -4-(-10) all equal -6).
5. **You add $2 to a piggy bank and add triple the money you added the previous day for one month**: This sequence grows in a multiplicative manner (tripling), making it non-arithmetic.
Based on this analysis, the examples of an arithmetic sequence are:
- **You start at an elevation of 12,000 feet and climb down 1,000 feet per day.**
- **20, 14, 8, 2, −4, −10.**
So, the correct selections are those two statements.