The constant difference between any two consecutive terms in an Arithmetic Progression (AP) is called the common difference.
Understanding Arithmetic Progression (AP)
An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is a key characteristic of APs.
Common Difference (d)
The common difference (d) is the constant value that is added to each term in an arithmetic progression to obtain the next term. According to the reference material provided, this common difference is crucial for understanding and working with arithmetic progressions.
- It can be positive, negative, or zero.
- It is used to find any term in the sequence.
Formula for the nth term of an AP
As mentioned in the reference, the general formula for finding the nth term (Tn) of an AP is:
Tn = a + (n-1)d
Where:
Tnis the nth term.ais the first term.nis the term number.dis the common difference.
Example
Let's consider the AP: 2, 5, 8, 11, 14,...
In this case:
- The first term (a) is 2.
- The common difference (d) is 5 - 2 = 3 (or 8 - 5 = 3, and so on).
To find the 10th term (T10):
T10 = 2 + (10 - 1) 3 = 2 + 9 3 = 2 + 27 = 29
Therefore, the 10th term is 29.
Summary
| Term | Description |
|---|---|
| Arithmetic Progression (AP) | A sequence where the difference between consecutive terms is constant. |
| Common Difference (d) | The constant difference between consecutive terms in an AP. |
| Formula for nth term | Tn = a + (n-1)d |
