Arithmetic progression-type of number series

 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

Different types of the number series

 

 Each series of numbers has a logical
relation / pattern to which the
successive terms are associated
based on this logical mathematical
relation we find the next term of the
sequence of numbers.

Many patterns are used in number
series and depending on the pattern
we have many different types of
number series

 To answer the question you must
first find the pattern / patterns.
Below we present the different
types of number series

 

• Simple series

•  Arithmetic Progression AP
  
• Geometric Progression  GP
  
• Combination AP and GP
• Two stage type series
• Perfect square series
• Perfect cube series
• Alternate series
• Mixed series

 

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 Number series basic concept
Number series types for competitive exams
Detailed examples for each type of number series