Introduction to Number Series Notes | EduRev

Number series is a form of sequence*, where some numbers are mistakenly put into the series of numbers and some number is missing in that series, we need to observe first and then find the accurate number to that series.

*Sequence is the list of numbers written in the specific order.
  For ex.  1, 4, 9, 16, 25, 36……..

Some Common Types and Their Tricks: 
Type 1 - Addition / Subtraction or Multiplication/Division

Example 1:  19, 23, 39, 75, _, 239

Most common trick to solve a number series is to solve by checking difference between two adjacent numbers, but difference could not only lead to addition/subtraction but it can also be with multiplication/division.
Therefore, to check whether to think addition wise or multiplication wise in increasing sequence one must make assumption with the help of difference between first and last number of the given sequence.

• If the difference seems to be less according to the number of steps used to make last number from first than we should check addition
• If the difference seems to be large or too large one must check multiplication trick between the adjacent numbers

In the Exercise 1. given above, difference between first no. (19) and last number (239) is 220.
Now a question will arise how we will assume whether the difference is more or less. We will assume it by keeping in mind number of steps required to start from first number till last number In Ex 1. 19 becomes 239 in five steps, because there are four more numbers between them, one of which we have to find out.
Difference of 220 between 19 and 239 in five steps logically giving priority to addition over multiplication in an increasing sequence like this.
75+64 = 139, 139+100 = 239          
139 is correct answer

Example 2: 10, 31, 95, 288, ___, 2609
As we can see in above ex. Difference between first number (10) and last number (2609) is 2599 in five steps, which indicate us to check multiplication trick between the numbers.
Note : While checking multiplication trick always start from right end of the sequence.

(288*3) + 4 = 868, is the correct answer.

Example 3: 30, 34, 43, 59, 84, 120,?
(1) 169
(2) 148
(3) 153
(4) 176
(5) None of these
Ans. (1)
Solution:
The given pattern is:
+22, 32, +42, + 62, +72
So, missing term is 169=120 +72

Example 4: 40, 54, 82, ?, 180 ,250
(1) 142
(2) 124
(3) 136
(4) 163
(5) None of these
Ans. (2)
Solution:
The pattern is: +14, + 28, + 42, + 52, + 70
So, missing term is 82 + 42 = 124

Example 5: 0, 1,3,8,18,35,264
(1) 62
(2) 35
(3) 18
(4) 8
(5) None of these
Ans. (1)
Solution: 
The pattern is +(02+1), +(12+1), + (22+1) ,+ (32+1), + (42+1), + (52+1)
So, 264 is wrong and must be replaced by 35 + (52+1) = 62

Example 6: 1, 9, 125, 49, 729, 121, 2147
(1) 2147
(2) 729
(3) 125
(4) 1
(5) None of these
Ans. (1)

Example 7: 5531, 5506, 5425, 5304, 5135, 4910, 4621
(1) 5531
(2) 5425
(3) 4621
(4) 5135
(5) 5506
Ans. (1)
Solution:
The number should be 5555 in place of 5531.
-72, -92, -112, -132, -152, -172…

Example 8: 6, 7, 9, 13, 26, 37, 69
(1) 7
(2) 26
(3) 69
(4) 37
(5) 9
Ans. (2)
Solution:
The number should be 21 in place of 26.
+1, +2, +4, +8, +16, +32

Example 9: 1, 3, 10, 36, 152, 760, 4632
(1) 3
(2) 36
(3) 4632
(4) 760
(5) 152
Ans. (4)
Solution:
The number should be 770 In place of 760.
×1 +2, ×2 +4, ×3 +6, ×4 + 8, ×5 +10, ×6 + 12, …

Example 10: 4, 3, 9, 34, 96, 219, 435
(1) 4
(2) 9
(3) 34
(4) 435
(5) 219
Ans. (1)
Solution: 
The series is 02+ 4, 12+2, 32+0, 62-2, 102-4, 152- 6,212 – 8…
Hence, 435 should be replaced with 433

Example 11: 157.5 45 15 6 3 2 1
(1) 1
(2) 2
(3) 6
(4) 157.5
(5) 45
Ans. (1)
Solution: 
The number should be 2 in place of 1.
3.5, 3, 2.5, 2, 1.5, 1, .

Type 2:  Perfect Square or Perfect Cube : 

Question: 4, 18, 48, 100, 180, ___.
In case if Type-1 is not applicable in a sequence, then in the next step we must compare given numbers or their differences to square or cube of natural numbers, as in the above example.

Therefore, (7)3-(7)2 = 294, is the correct answer.

Perfect Square Series:

This Types of Series are based on square of a number which is in same order and one square number is missing in that given series.

Example 1: 841, ?, 2401, 3481, 4761
Answer : 29², 39², 49², 59², 69²

Example 2: 1, 9, 25, ?, 81, 121
Answer : 1², 3², 5², 7², 9², 11²

Example 3: 289, 225, 169, ?, 81
Answer: 17², 15², 13², 11², 9²

Perfect Cube Series:
This Types of Series are based on cube of a number which is in same order and one cube number is missing in that given series.
Example 1: 3375, ?, 24389, 46656, 79507
Answer : 15³, 22³, 29³, 36³, 43³
(Each cube digit added with seven to become next cube number)

Example 2: 729, 6859, 24389, ?, 117649, 205379
Answer : 9³, 19³, 29³, 39³, 49³, 59³

Example 3: 1000, 8000, 27000, 64000, ?
Answer: 10³, 20³, 30³, 40³, 50³

Type 3: Factorisation / Prime factorisation 
If Type 1 and Type 2 is not applicable in a sequence, one must try to make factors of the numbers in the next step.

Example 1: 6, 15,35,77,143, __.
In the above example all the previous tricks are not applicable to get answer. Hence, We will make factors of the given numbers
(2,3,5,7,11,13) all are prime numbers in ascending order.
Hence, 13*17 = 221, is the correct answer.

Example 2: – 31, 41, 47, 59, __.
In this ex. All the previous tricks are not applicable and then if we think of factorization we will found all the numbers are prime. Two adjacent numbers in the sequence are alternate prime numbers. Therefore, 67 is the correct answer

Type 4 -   Fibonacci series 
A series in which a number is made by using previous two numbers is called Fibonacci series.

Example : 1, 4, 5, 9, 14, 23, ___
In the above sequence all the numbers are sum of previous two numbers.
Therefore, 23+14 = 37, is the correct answer.

Type 5 – SUM OF DIGITS 

Example 1:
In the above sequence, difference between two numbers is the sum of digits of the first number.
Hence, 89+17 = 106, is the correct answer.

Example 2: 
All the numbers are multiplied by their sum or added by their sum alternately.
Therefore, 11788+25 =11813, is the correct answer.

Type 6 – ALTERNATE PATTERN SERIES
When numbers given as a hint in a questions are more or when a question ask two numbers of a series or same number come twice in a series, these all give hint to alternate pattern series.

Example 1: 
So, numbers are 12+5=17,53-6=47
Ans-17,47

Example 2:

So, the number is 24+3=27
Ans- 27

TYPE 7 - DECIMAL PATTERN SERIES
When the numbers of the sequence are given in the decimal form is decimal pattern series.

Example 1: 
So, the answer is 18*.8 = 14.4

Example 2:  16, 24, 60, 210, 945, __
The pattern is:
16*1.5 = 24
24*2.5 =60
60*3.5 = 210
210*4.5 = 945
945*5.5 = 5197.5

TYPE 8  BRACKET PATTERN SERIES
While using bracket pattern we multiply first oustside and either add or sub based on given no.

Example 1: 3, 28, 180,  ____,  3676
The pattern is :
(3+1)*7 = 28
(28+2)*6 =180
(180+3)*5 = 915
(915+4)*4 = 3676
Ans – 915

Example 2: 37, 31, 52, 144, __, 2810
The pattern is :
(37-6)*1=31
(31-5)*2=52
(52-4)*3=144
(144-3)*4=564
(564-2)*5=2810
Ans – 564

TYPE-9 DUAL PATTERN SERIES
Example :
15,   9,    8,     12,       36,       170
19,   a,    b,     __,       d,           e,
The pattern is :
(15-6)*1=9
(9-5)*2=8
(8-4)*3=12
Similarly:
(19-6)*1=13
(13-5)*2=16
(16-4)*3=36
Ans – 36

TYPE 10 - FACTORIAL BASED SERIS
This is latest pattern question asked in latest exams

Example 1: 
Ans – 33

Example 2: 
Ans - 606+721=1327