Select ALL of the following which are examples of an arithmetic sequence.
Responses
−2, −4, −8, −16, −32
−2, −4, −8, −16, −32
You add $1 to a piggy bank and add double the money you added the previous day for one month.
You add $1 to a piggy bank and add double the money you added the previous day for one month.
6, 11, 15, 21, 26, 30
6, 11, 15, 21, 26, 30
12, 9, 6, 3, 0, −3
12, 9, 6, 3, 0, −3
You start at an elevation of 15,000 feet and climb down 2,000 feet per day.
You start at an elevation of 15,000 feet and climb down 2,000 feet per day.
−2, −4, −8, −16, −32
6, 11, 15, 21, 26, 30
12, 9, 6, 3, 0, −3
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. To determine if the given examples are arithmetic sequences, we need to check if the difference between consecutive terms is constant.
Let's examine each example:
1. −2, −4, −8, −16, −32
The common difference between consecutive terms is -2, so this is an arithmetic sequence.
2. You add $1 to a piggy bank and add double the money you added the previous day for one month.
This is not an arithmetic sequence since there is no constant difference between consecutive terms.
3. 6, 11, 15, 21, 26, 30
The common difference between consecutive terms is 5, so this is an arithmetic sequence.
4. 12, 9, 6, 3, 0, −3
The common difference between consecutive terms is -3, so this is an arithmetic sequence.
5. You start at an elevation of 15,000 feet and climb down 2,000 feet per day.
This is not an arithmetic sequence since there is no constant difference between consecutive terms.
Therefore, the examples (1), (3), and (4) are arithmetic sequences.