You're working with a
linear sequence given by the formula:
>
Term = 3n + 2
Where:
-
n is the
position in the sequence (starting at n = 1, 2, 3, ...)
-
Term is the value of the term at that position.
---
Step 1: Fill in the table
We’ll calculate the first few terms using the formula
Term = 3n + 2.
Let’s compute for positions
n = 1 to 6 (since the grid goes up to x=6):
| Position (n) | Term = 3n + 2 |
|--------------|----------------|
| 1 | 3(1) + 2 = 5 |
| 2 | 3(2) + 2 = 8 |
| 3 | 3(3) + 2 = 11 |
| 4 | 3(4) + 2 = 14 |
| 5 | 3(5) + 2 = 17 |
| 6 | 3(6) + 2 = 20 |
✔ So your completed table should look like this:
| Position | 1 | 2 | 3 | 4 | 5 | 6 |
|----------|----|----|----|----|----|----|
| Term | 5 | 8 | 11 | 14 | 17 | 20 |
---
Step 2: Plot the points on the graph
You are to plot these as
coordinates (x, y) where:
>
x = position (n)
>
y = term
So your points are:
- (1, 5)
- (2, 8)
- (3, 11)
- (4, 14)
- (5, 17)
- (6, 20)
On the grid:
- The
x-axis goes from 0 to 6 → matches your positions.
- The
y-axis goes from -5 to 25 → plenty of room for your terms (up to 20).
Plot each point carefully with a pencil:
- At x=1, go up to y=5 → mark point
- At x=2, go up to y=8 → mark point
- ... and so on.
Since this is a
linear sequence, the points will lie on a
straight line.
---
Step 3: Draw the line (optional but helpful)
After plotting all 6 points, you can lightly draw a straight line through them to show the pattern. This helps visualize how the sequence grows linearly.
---
✔ Final Answer Summary:
Table:
| Position | 1 | 2 | 3 | 4 | 5 | 6 |
|----------|---|---|---|---|---|---|
| Term | 5 | 8 | 11| 14| 17| 20|
Coordinates to plot:
(1,5), (2,8), (3,11), (4,14), (5,17), (6,20)
Graph: Plot these points on the grid and connect them with a straight line (if required).
---
💡
Why this works: The formula
3n + 2 is linear — it increases by 3 each time (common difference). That’s why the graph is a straight line with slope 3 and y-intercept 2 (if extended to n=0).
Let me know if you’d like to see a sketch or further explanation!
Parent Tip: Review the logic above to help your child master the concept of graphing sequences worksheet.
