Final answer:
Three different arithmetic sequences that include the terms 4 and 16 can be created by varying the common difference and positions of the terms within the sequence. Examples include sequences with common differences of 3, 4, and 1.5.
Step-by-step explanation:
To create three different arithmetic sequences that include the terms 4 and 16, we need to determine the common difference d and the position of the two known terms within the sequence. In an arithmetic sequence, each term is the sum of the previous term and the common difference d.
To illustrate, here are three different arithmetic sequences that contain the terms 4 and 16:
- Sequence A: 1, 4, 7, 10, 13, 16
Here, the common difference d is 3. The terms 4 and 16 are the 2nd and 6th terms respectively. - Sequence B: 4, 8, 12, 16
In this case, the common difference d is 4. The terms 4 and 16 are the 1st and 4th terms respectively. - Sequence C: 4, 5.5, 7, 8.5, 10, 11.5, 13, 14.5, 16
Here, the common difference d is 1.5. The terms 4 and 16 are the 1st and 9th terms respectively.
Each sequence shows how varying the common difference and the terms' positions can lead to distinct sequences while still including the given terms, 4 and 16.