<h2>What is arithmetic progression</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 term

s 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

Sequence  4, 9, 14, 19, 24

Is an AP  with d=5

Sequence   8, 5, 2, -1, -4

is an AP with difference d=-3

 

 

If the initial term of an arithmetic progression is ${\displaystyle a_{1}}$

and the common difference of successive members is ${\displaystyle d}$,

 then the ${\displaystyle n}$-th term of the sequence (${\displaystyle a_{n}}$) is given by:

${\displaystyle \ a_{n}=a_{1}+(n-1)d}$,

 

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