No, the common ratio is not the difference between two consecutive numbers in an arithmetic progression.
It's important to distinguish between arithmetic and geometric progressions:
-
Arithmetic Progression: A sequence where the difference between consecutive terms is constant. This constant difference is called the common difference.
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Geometric Progression: A sequence where the ratio between consecutive terms is constant. This constant ratio is called the common ratio.
| Feature | Arithmetic Progression (AP) | Geometric Progression (GP) |
|---|---|---|
| Definition | Constant difference between terms | Constant ratio between terms |
| Key Value | Common Difference (d) | Common Ratio (r) |
| Calculation | d = an - an-1 | r = an / an-1 |
| Example Sequence | 2, 4, 6, 8... (d=2) | 2, 4, 8, 16... (r=2) |
Arithmetic Progression Explained
According to the provided reference, the common difference in an arithmetic progression is found by subtracting a term from its subsequent term. The formula to find the common difference (d) is:
d = an - an-1
Where:
- an is the nth term in the sequence
- an-1 is the term before the nth term
Example:
Consider the arithmetic progression: 3, 7, 11, 15...
- To find the common difference, subtract any term from the term that follows it.
- 7 - 3 = 4
- 11 - 7 = 4
- 15 - 11 = 4
Therefore, the common difference (d) is 4.
Common Ratio Example
Let's consider a geometric progression: 2, 6, 18, 54...
To find the common ratio:
- 6 / 2 = 3
- 18 / 6 = 3
- 54 / 18 = 3
Therefore, the common ratio (r) is 3.
