The Steady Step: Building Arithmetic Progressions
Slide 'a' and 'd' to see how a constant difference creates a predictable pattern.
Equation
y = 3 + (x - 1)*2
Graph
Table
| x | y |
|---|---|
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
| 5 | 11 |
| 6 | 13 |
| 7 | 15 |
| 8 | 17 |
| 9 | 19 |
| 10 | 21 |
What this lesson covers
What you do
You shape the function y = a + (x - 1)*d and watch the graph answer.
Challenges to clear
- Set a = 3. Find the common difference d so that the 5th term (x = 5) is exactly 23.
- With the same d: the 10th term lands on 48 — steady steps, predictable future.
- Set the first term to 4.
- Now find the common difference that puts the 6th term at 34 — five steps from the start, not six.
Check yourself
In the formula y = a + (n-1)*d, what does 'd' represent?
- The starting value of the sequence
- The constant difference added to get the next term — correct
- The total number of terms in the sequence
- The product of the first and last terms
Think about it
- What happens to the steepness of the line when you increase d?
- How does changing a move the entire pattern up or down?