Give the next three terms of the sequence 5, 9, 13, 17, 21, 25,... Then graph the sequence.

5,_,_,17

To find the next terms of the sequence, we notice that each term is increasing by 4. So, to find the next terms, we add 4 to the last term:

25 + 4 = 29
29 + 4 = 33
33 + 4 = 37.

Therefore, the next three terms of the sequence are 29, 33, and 37.

To graph the sequence, we can represent the terms on the y-axis and the position of each term on the x-axis. Let's assume the first term (5) is at position 1. Here's the graph of the sequence:

Term 1: (1, 5)
Term 2: (2, 9)
Term 3: (3, 13)
Term 4: (4, 17)
Term 5: (5, 21)
Term 6: (6, 25)
Term 7: (7, 29)
Term 8: (8, 33)
Term 9: (9, 37)

Now let's plot these points on a graph:

```
|
40 | ●
|
35 | ●
|
30 | ●
|
25 | ●
|
20 | ●
|
15 | ●
|
10 | ●
|
5 | ●
|
0 ──┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼───┼─
1 2 3 4 5 6 7 8 9 10 11 12 13 14
```

The points on the graph represent the terms of the sequence, and the dots represent each term.

To find the next terms of the given sequence, notice that each term is obtained by adding 4 to the previous term. Therefore, to find the next terms, we continue this pattern:

5 + 4 = 9
9 + 4 = 13
13 + 4 = 17

Hence, the next three terms of the sequence are 9, 13, and 17.

To graph the sequence, we can plot the terms of the sequence on a coordinate plane. Let's use the x-axis to represent the position of each term in the sequence, and the y-axis to represent the value of each term.

The given sequence starts with 5, which would be represented as (1, 5) on the graph. The second term, 9, would be represented as (2, 9). Similarly, the third term 13 would be (3, 13), the fourth term 17 would be (4, 17), the fifth term 21 would be (5, 21), and the sixth term 25 would be (6, 25).

Here is a table illustrating the coordinates of each term:

Term | Position (x) | Value (y)
-------------------------------
1 | 1 | 5
2 | 2 | 9
3 | 3 | 13
4 | 4 | 17
5 | 5 | 21
6 | 6 | 25

Plotting these points on the coordinate plane and connecting them with a line will display the graph of the sequence.

a=5 and d=4, so the graph is just the line

y=5+4(x-1)=4x+1

all arithmetic sequences are just straight lines, because of the constant d (the slope of the line)