Spot the Geometric Pattern
Divide each term by the previous one. If you get the same ratio every time, it is a GP.
Equation
y = 2 * 0.5^(x - 1)
Graph
Table
| x | y |
|---|---|
| 1 | 2 |
| 2 | 1 |
| 3 | 0.5 |
| 4 | 0.25 |
| 5 | 0.13 |
| 6 | 0.06 |
What this lesson covers
What you do
You shape the function y = a * r^(x - 1) and watch the graph answer.
Challenges to clear
- Make the sequence 2, 6, 18, 54, ... (a = 2, common ratio 3).
- Divide any term by the previous: 54/18 = 3 — check the 4th term is 54.
- Make the sequence 3, 6, 12, 24 … Start it at 3.
- Now the ratio: the 5th term is 48. Divide any term by the one before it and you get the same number every time.
Check yourself
How do you check if 5, 15, 45, 135 is a GP?
- Divide consecutive pairs: 15/5 = 3, 45/15 = 3, 135/45 = 3. Same ratio every time -> GP with r = 3. — correct
- Check that the differences are equal (that is an AP).
- See if the numbers are increasing.
- Sum them up and check if the total is divisible by 5.
Think about it
- Slide r. Watch how the table values explode (r > 1) or shrink (r < 1).