Arithmetic Progression (AP):
An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the preceding term except the first term.
This fixed number is called the common difference of the AP. It can be positive, negative or zero.
Where, the first term is denoted by 'a' and the common difference is denoted by 'd'
Example:
\(5\), \(15\), \(25\), ...
In the above example
The first term, \(a=5\)
The common difference \(d = 10\)
How to find the common difference?
Consider the above example,
\(5\), \(15\), \(25\),...
Common difference \(=\) a term \(-\) its preceeding term.
Common difference, \(d = second term - first term\)
\(d = 15 - 5\)
\(d = 10\)
General form of an AP:
\(\text{a, a + d, a + 2d, a + 3d, . . .}\)
represents an arithmetic progression where 'a' is the first term and 'd' the common difference. This is called the general form of an AP.
Also it can be written as \(a_1, a_2, a_3,....\)
Types of AP:
Finite AP:
If there is a last term in the given AP, then it is called an finite AP.
Last term can be denoted as 'l'.
Infinite AP:
If there is no last term in the given AP, then it is called as infinite AP.