## Number & Letter Series

### Number & Letter Series

A series is a sequence of numbers/alphabetical letters or both which follow a particular rule. Each element of series is called ‘term’. One has to analyze the pattern and find the missing term or next term to continue the pattern.  some cases,a series is given where one of the terms is incorrect,one has to identify the wrong term.

In number series, relationship between the terms is of any kind. Below are some examples:

1. Consecutive even numbers as difference. For instance:13, 15, 19,25, 33,43..
Here the successive differences between the consecutive terms are 2,4, 6,8, 10..
2. Consecutive odd numbers as difference. For instance:22, 25,30,37, 46,57..
Here the successive differences between the consecutive terms are 3,5, 7,9, 11..
3. Consecutive Prime numbers
For instance:23, 29,31,37, 41,43, 47..
Here the terms are consecutive prime numbers
4. Square of numbers as difference. For instance:91, 87,78,62, 37,1..
Here the successive differences between the consecutive terms are 4,9, 16, 25,36 .i.e.12,22,32,42,52, 62..
5. Cubes of numbers as difference.
For instance:4, 5, 13, 40, 104,229..Here the successive differences between the consecutive terms are 1,8, 27, 64,125.. i.e. 13, 23,33, 43,53
6. Fibonacci series – Series where a term starting from the 3rd term is the sum of the previous two terms. For instance:2, 5, 7, 12, 19, 31, 50..
7=5+2,12=7+5, 19=12+7,31=19+12,50=31+19..
7. Arithmetic or geometric progressions. For instance:25, 42,59,76, 93, 110..
Here the difference between the consecutive terms is 17. 8,20, 50, 125,312.5
Here the ratio between the consecutive terms is 2.5.
8. Combination of multiplication and addition. For instance:3, 4, 10, 33, 136,685..
Here the pattern is 3 x 1 + 1= 4,4 x 2 + 2 = 10, 10 x 3 + 3 = 33, 33 x 4 + 4 = 136, 136 x 5 + 5 = 685..

#### Types of questions:

(I) Find Missing/Next number of the series

Here a series is a given with a missing term in between or at the end.One has to find the missing term.

Solved Examples:

Find the next term in the following number series: 5, 10, 17, 28,41, 58 ?
The differences between the successive terms are 5, 7, 11, 13, 17,i.e. successive prime numbers. So the next difference must be 19.Hence the next term is 58+19 = 77
Find the missing term in the following number series: 3, 7, 16, ?, 57, 93, 142
The series is 3 + 22 = 7, 7 + 32 = 16, 16 + 42 = 32, 32 + 52 = 57,57 + 62 = 93, 93 + 72 = 142

Hence the missing term is 32.

(II) Find Wrong number of the series

Here a series that follows a particular rule is a given. One of the terms of the series does not follow the rule. One has to find the wrong term.

Solved Examples:

In the following number series,one of the terms is wrong.Identify that term. 7, 12, 20, 31,44, 62, 82
The pattern is: 7+5=12, 12+8=20,20+11=31,31+14=45, 45+17=62, 62+20=82, i.e. successive differences increasing by 3.

Hence the wrong term is 44.

Tips for solving number series problems:

Number series problems are either the low hanging fruits or the speed breakers depending on how much time one takes to identify the pattern.
– Try applying the above rules to see which one is applicable.

– Memorize the squares and cubes of few initial numbers,say upto 20.

– If the pattern can be identified within 15-20 seconds try computing the answer.

– Do not spend too much time on a question.

– Leave the difficult problems,you may get back to them later.