 ## Number Series Concept

Candidates who are going to apply for Bank, SSC and UPSC Exam, they might know that the chapter of Number series is especially crucial because so many questions asked in the exam from this chapter. So, here we are providing you significant number series short tricks, formulas and concepts on Number Series Questions which are usually asked in all these Exams. Apply these below given short tricks to solve questions in least time. These shortcuts will be very helpful for your upcoming Bank, SSC Exam.

Number series chapter is very scoring and less time consuming, and to make the chapter easy for you all, we are providing you some vital Maths Tricks which will definitely make the chapter easy for you all. Questions on number series are connected with each other and formerly you have acknowledged this pattern, solving the question becomes very easy. Just the once you have recognized the pattern then relate this to the number before/ after the missing number in the sequence to get the preferred respond.

Common Patterns in "Number Series" Questions

Prime Numbers- When numbers are a series of prime numbers (a natural number which is greater than 1 and has no positive divisors other than 1 and the number itself)

For example - 11, 13, 17, 19

Squares/ Cubes- When numbers are a series of perfect square or cube roots

For example - 81, 100, 121, 144, 169

Patterns in differences- Calculate the differences between the numbers given in the series provided in the question. Then try to observe the pattern in the new set of numbers that you have obtained after taking out the difference.

For example - 2, 5, 8, 11, 14 (here the difference between the numbers is 3, hence the next number will be 17)

Pattern in alternate numbers- when there is a pattern between every alternate or third number in the series

For example - 2, 9, 5, 1, 8, 15, 11

Geometric series- when each successive number in the series is obtained by multiplying or dividing the previous number by a fixed number.

For example - 5, 45, 405, 3645

Odd one out- when all but one number is part of a series

For example - 5, 10, 12, 15, 20 (Here all numbers except, 12 are multiples of 5)

Pattern in adjacent number- when adjacent numbers in the series changes based on a logical pattern
For example - 2, 4, 12, 48 (Here the first number is multiplied by 2, the second number by 3 and the third number by 4)

Complex series- In some patterns the differences between numbers is dynamic rather than being fixed, but there still is a clear logical rule

For example - 3, 4, 6, 9, 13, 18 (Here you can add 1 to the difference between two adjacent items. After the first number add 1, after the second number add 2 and after the third number you can add 3)
Using two or more basic arithmetic functions: in some series more than one operation (+, -, ÷, x) is used

For example - 5, 7, 14, 16, 32 (here you can add 2, multiply by 2, add 2, multiply by 2, and so on)

Cube roots/ square roots- when the numbers are a series of cube roots and square roots

For example - 512, 729, 1000 (here the next number in the series will be 1331)

What is Number Series?

Number series is a form of numbers in a certain string, where some numbers are incorrectly put into the series of numbers and some number is missing in that series, we need to scrutinize first and then find the precise number to that series of numbers.

Shortcut of "Number Series"
• Questions on number series give you a series of numbers which are all connected to each other. Once you have identified this pattern, solving the question becomes very simple.
• This pattern can be of different kinds. Check the section below for a list of common patterns which are frequently present in the Bank Exam.
• Once you have acknowledged the pattern, apply it to the number before/ after the missing number in the series to get the desired answer.
Some Important Number Series Questions:

Question 1: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces-

1, 4, 9, 16, 25, x

A.35
B. 36
C. 48
D. 49

Justification: The numbers are 12, 22, 32, 42, 52.
.'. Missing number = 6= 36.

Question 2: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces-

20, 19, 17, x, 10, 5

A. 12
B. 13
C. 14
D. 15

Justification: The Pattern is - 1, - 2,.
.'. Missing number = 17 - 3 = 14.

Question 3: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces-

2, 3, 5, 7, 11, x, 17

A. 12
B. 13
C. 14
D. 15

Justification: Clearly, the given series consists of prime numbers starting from 2. The prime number after 11 is 13.
So, 13 is the missing number.

Question 4: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces-

6, 11, 21, 36, 56,

A. 42
B. 51
C. 81
D. 91

Justification: The pattern is + 5, + 10, + 15, + 20,..
.'. Missing Number = 56 + 25 = 81

Question 5: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces-

1, 6, 13, 22, 33,

A. 44
B. 45
C. 46
D. 47

Justification: The pattern is + 5, + 7, + 9, + 11,.
.'. Missing number = 33 + 13 = 46.

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Question 6: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces-

3, 9, 27, 81,

A. 324
B. 243
C. 210
D. 162

JustificationEach term of the given series is obtained by multiplying its preceding term by 3.
.'. Missing number = 81 * 3 = 243.

Question 7: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces-

1, 9, 17, 33, 49, 73,

Option:
A. 97
B. 98
C. 99
D. 100

Justification: The pattern is + 8, + 8, + 16, + 24,...
.'. Missing number = 73 + 24 = 97

Question 8: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces.:

2, 5, 9, x, 20, 27

A. 14
B. 16
C. 18
D. 24

Justification: The pattern is + 3, + 4,...
.'. Missing number = 9 + 5 = 14.

Question 9: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces-

5, 9, 17, 29, 45,

A. 60
B. 65
C. 68
D. 70

Justification:
The pattern is + 4, + 8, + 12, + 16, ..
.'. Missing number = 45 + 20 = 65.

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Question 10: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces-

3, 7, 15, 31, 63,

A. 92
B. 115
C. 127
D. 131

Justification: Each number in the series is the preceding number multiplied by 2 and then increased by 1.

Thus, (3 * 2) + 1 = 7,
(7 * 2) + 1 = 15
(15 * 2) + 1 = 31 answer so on
.'. Missing number = (63 * 2) + 1 =127.

Question 11: In following question, a number series is given with one term missing. Choose the correct alternative that will same pattern and fill in the blank spaces.:

1, 6, 15, x, 45, 66, 91

A.    25
B.    26
C.    27
D.   28

Justification: The pattern is + 5, + 9, .., + 21, + 25
.'. Missing number = 15 + 13 = 28.

Different types of Number Series

Square series: These are also known as perfect square series which are based on square of a number in same order. In exam it can be missing square or mistakenly Put Square in series.

Example:  289, 324, 361, 400,?
Answer: 289 = 172, 324 = 182, 361 = 192, 400 = 202, 441 = 212

Cube series: these types of series based on perfect cube. In exam there can be missing cube or mistakenly put cube in number series.

Example: 1728, 2197, 2744, 3375,?

Answer: 1728 = 123, 2197 = 133, 2744 = 143, 3375 = 153, 4096 = 163

Geometric Series: It is the sequence of numbers based on ascending or descending order. Next number is obtaining by multiplying or dividing the previous number or vice versa.

Example: 9, 54, 324, 1944,?

Answer: 9 x 6 = 54, 54 x 6 = 324, 324 x 6 = 1944, 1944 x 6 = 11664

Mixed Series: This type of number series can be used various method. In this number may be given in addition, subtraction, multiplication and division in the alternate numbers. It is created according to any non-conventional rule.

Example: 10, 31, 94, 283,?

Answer: 10 x 3 = 30 + 1 = 31,
31 x 3 = 93 + 1 = 94,
94 x 3 = 282 + 1= 283,
283 x 3 = 849 + 1 = 850,
So the missing number is 850.

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