**Full Concept of Number Series**

**Number series can be defined as an arrangement of numbers in a certain order, where some numbers are wrongly put into the series of numbers and some number is missiang in that series, We need to observer and find the accurate number to the series of numbers.**

**OR****A Series is a sequence of numbers obtained by some particular predefine rule and also applying that predefined rule it is possible to find out the missing or wrong number in a sequence. The missing or wrong number may be at the beginning or middle or at the end of sequence/next term of series.**

**Different Types of Number Series:**

**Even Series:****Odd Series:****Prime Series:****Square Series:****Cube Series:****Arithmetic Series:****Geometric Series:****Geometric - Arithmetic Series (GP-AP Series):****Twin Series:****Decimal Series:****Fractional Series:****Half Pattern series:****Multiplication & Addition Series:****Multiplication and Subtraction Series:****Divisible series:****Ration Series:****Difference Series:****Series of Date or Time:****Series of LCM or HCF:****One Line Series:****Two Line Series:****Follow Product series:****By Use of digit-Sum Series:****Odd Number out Series:****Mixed Series:-**Series based on a given logic, series based on Square & Cube, etc..

**1.)**

__Even Series:__The series in which all the numbers are even numbers followed by a sequence, is known as even series.**Example: 2 , 4 , 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 etc.**

**2.)**

__Odd Series:__The series in which all the numbers are odd numbers followed by a sequence, is known as odd series.**Example: 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 etc.**

**3.)**

__Prime Series:__The series in which all the numbers are prime numbers followed by a sequence, is known as prime series.**Example: 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 etc.**

**4.)**

**Square Series:****The series in which all the numbers are squares of natural numbers followed by a sequence is known as square series.(**This series can be formed by squaring every successive numbers.)

**Example: 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 etc.**

**5.)**This series can be formed by cubing every successive numbers.)

__Cube Series:__The series in which all the numbers are the cube of natural numbers followed by a sequence, is known as cube series. (**Example: 1 , 8 , 27 , 64 , 125 , 216 , 343 , 512 , 729 etc.**

**6.)**A succession of numbers is said to be in Arithmetic series if the difference between any term and the term preceding it is constant throughout.)

__Arithmetic Series:__The series in which the difference between each successive terms is constant, is known as arithmetic series. (**Example: 84 , 80 , 76 , 72 , 68 , 64 , 60 , 56 , 52 , 48 , 44 etc.**

**Example : 1 , 4 , 7 , 10 , 13 ,**........ , ..........

**(A.)**(The series in which the difference is constant after two steps, is known as two tier arithmetic series.)

__Two Tier / Second Degree Arithmetic Series:__A series in which the difference between two of successive terms themselves are in the arithmetic series, form a second degree arithmetic series.

Example: 2 , 6 , 12 , 20 , 30 , 42 , 56 , 72 , 90 , 120 etc.

Example: 2 , 6 , 12 , 20 , 30 , 42 , 56 , 72 , 90 , 120 etc.

**Example: 2 , 3 , 6 , 11 , 18 ,**............

**(B.)**

__Three Tier / Third Degree Arithmetic Series:__**A series in which the difference of the successive terms form a second degree Arithmetic series is termed as third degree Arithmetic series.**(The series in which the difference is constant after three steps, is known as three tier arithmetic series.)

Example: 336 , 210 , 120 , 60 , 24 , 6 , 0 etc.

Example: 336 , 210 , 120 , 60 , 24 , 6 , 0 etc.

**Example : 20 , 30 , 42 , 59 , 84 , 120 , ?**

**7.)**

__Geometric Series____:__

**The series in which the ratio between each successive term is constant, is known as geometric series.**(A succession of numbers is said to be in geometric series if the ratio of any term and the term preceding it, is constant throughout.)

**Example: 5 , 45 , 405 , 3645 , ?**

__Note:__This type of series are based on ascending or descending order of numbers and each successive number is obtain by multiplying or dividing the previous number with a fixed number.**(A.)**

__Two stage type Series:__A two tier Arithmetic series is one in which the differences of successive numbers themselves from an arithmetic series.**Example: 4 , 5 , 9 , 16 , 26 , 39**

**Example : 4 , 12 , 36 , 108 , 324 , ..............**

**8.)**

**Geometrico - Arithmetic Series (GP-AP/AP-GP Series):**

**The series in which we can get the next term first by multiplying/dividing and then by adding/subtracting, is known as GP-AP series.**(It is just reverse of Arithmetico - Geometric Series.)

**Example: 3 , 7 , 15 , 31 , 63 , 127 , 255 , 511 , 1023 etc.**

**(9.)**

**Twin Series:**

**As the name suggests, it consists of two series combined into a single series. The alternating terms of this series form an independent series.**

**Example: 3 , 5 , 7 , 10 , 12 , 30 , ? , ?**

**(10.)**

**Decimal Series:****Series based on decimal number .**

**Example: 12 , 6.5 , 7.5 , 12.75 , 27.50 , ?**

**(11.)**Series based on Fraction number

__Fractional Series:__**Example: 12/15 , 7/15 , 2/15 , ? , -8/15**

**(12.)**

__Half Pattern Series:__**Example: 70 , 40 , 50 , 90 , 200 , ?**

**(13.)**

__Multiplication & Addition Series:__**Example: 5 , 13 , 29 , 61 , 125 , ?**

**(14.)**

__Multiplication and Subtraction Series:__**Example: 5 , 7 , 11 , 19 , 35 , ?**

**(15.)**Completely Divisible series

__Divisible series:__**Example: 12 , 12 , 18 , 45 , 180 , ?**

**(16.)**All terms while in increasing order multiplied

__Ration Series:__**Example: 336 , 168 , 84 , 42 , 21 , ?**

**(17.)**

__Difference Series:__**Example: 1348 , 1338 , 1318 , 1288 , 1248 , ?**

**(18.)**

__Series of Date or Time:__**Example:**

**05-01-96 , 27-01-96 , 18-02-96 , ? , 02-04-96**

**Example: 05.40 , 08.00 , 10.20 , ? , 3.00 , 5.20**

**(19.)**Some numbers followed by their LCM or HCF:

__Series of LCM or HCF:__**Example: 1 , 2 , 3 , 6 , 4 , 5 , 6 , 60 , 5 , 6 , 7 ,**___

**Example: 8 , 4 , 4 , 7 , 8 , 1 , 3 , 9 , 3 , 2 , 1 ,**___

**(20.)**

**One Line Series:**

**If the rate of increase/decrease is slow in a series, there must be addition or subtraction. So, the series is an**

**arithmetic series.**

**Example: 2 , 6 , 12 , 20 , 30 , 42 , 56 , 72 , .......**

**(21.)**

**Two Line Series:**

**If the rate of increase/decrease is slow, it is a form of arithmetic series. Take the difference between the first**

**term of the two lines. if the first term of second line is greater than the first term of first line, add the**

**difference with the required number of the first line. If the first term of second line is lower than the first**

**term of first line, subtract the difference from the required number of the first line.**

**Example: 128 , 124 , 118 , 110 , 100**

**100 , (A) , (B) , (C) , (D)**

**Find the value of (D).**

Some numbers followed by their product:__Follow Product series:__**Example: 2 , 3 , 6 , 18 , 108 , ?**

__By Use of digit-Sum Series:__**Example: 14 , 19 , 29 , 40 , 44 , ? , 59 , 73**

__Odd Number out Series:__Sometimes a group of numbers is written out.**Example: 22 , 44 , 88 , 132 , 165 , 191 , 242**

**(25.)**

**Mixed Series:****This types of series are more than one different order are given in a series which arranged in alternatively in a single series or created according to any non-conventional rule.**

**Example: 11 , 24 , 50 , 102 , 206 , ?**

**(A)**This series can be formed by squaring or cubing every successive numbers.

__Squares & Cubes mixed Series:__**Example : 4 , 6 , 256 ,**.........

**Example : 2 , 8 , 512 ,**.........

**Example : 4 , 27 , 16 , 125 , 36 , 343 ,**.........

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