Arithmetic Progression (AP):
- Definition: An arithmetic progression is a sequence of numbers where the difference between consecutive terms remains constant. This constant difference is known as the common difference (d).
- Example: 2, 5, 8, 11, 14…
- Common Difference (d): In this example, the common difference is 3, as each term is obtained by adding 3 to the previous term.
- General Term: The nth term of an arithmetic progression can be calculated using the formula:
Tn = a + (n-1)dwhere:- Tn is the nth term
- a is the first term
- n is the position of the term in the sequence
- d is the common difference
- Sum of n terms: The sum of the first n terms of an arithmetic progression can be calculated using the formula:
Sn = n/2 * (2a + (n-1)d)orSn = n/2 * (a + l)where:- Sn is the sum of the first n terms
- a is the first term
- n is the number of terms
- d is the common difference
- l is the last term