Is it an AP?
Use the formula to check if the difference between terms is constant.
Equation
y = 2 + (x-1)*3
Graph
Table
| x | y |
|---|---|
| 1 | 2 |
| 2 | 5 |
| 3 | 8 |
| 4 | 11 |
| 5 | 14 |
What this lesson covers
What you do
You shape the function y = a + (x-1)*d and watch the graph answer.
Challenges to clear
- Create an AP starting at 5 with a common difference of 2.
- Check the pattern: 5, 7, 9, 11 — the 4th term must be 11, constant gap throughout.
- Build the sequence 3, 7, 11, 15 … Start it at 3.
- Now find the common difference: the 5th term must be 19. The gap is the same every single step — that is what makes it an AP.
Check yourself
Which of these sequences is NOT an Arithmetic Progression?
In the formula y = a + (n-1)d, what does 'd' represent?
- 2, 4, 6, 8, ...
- 10, 7, 4, 1, ...
- 1, 4, 9, 16, ... — correct
- 5, 5, 5, 5, ...
- The first term of the sequence
- The total number of terms
- The constant difference between consecutive terms — correct
- The sum of all terms
Think about it
- If you increase d by 1, how does the gap between consecutive terms change?