<h2>Arithmetic progression-type of number series</h2>

 An arithmetic progression or arithmetic sequence 

is a sequence in which the difference between

 any two consecutive terms is constant.

 The difference between the consecutive terms

 is known as the common difference 

and is denoted by d.

 

If the first term is a  A(rithmetc) P(rogression)  is

a, a+d, a+2d, a+3d, a+4d

 Examples

3,5,7,9,11 is an AP

3, 3+2, 3+2+2, 3+2+2+2

Common difference is  d=2

 

If the initial term of an arithmetic progression is

and the common difference of successive members is ,

 then the -th term of the sequence () is given by:

,

 

Example

 

Sequence   3,7, 11, 15, 19, 23,  ...,...,....,...  

is an AP  first term  a1=3  with d=4

Sixth term 23=3+(6-1).4

What is the seventh term?

3+(7-1).4=3+6.4=3+24=27

 

 Different types of the number series