# Number Series Tricks

Number Series Tricks: Now Days, Cracking competitive examinations is the main goal of youth generation. Reasoning and Quantitative Aptitude is the main sections of competitive examination. Number Series is one of the most of important topic of reasoning aptitude test. We have given Number Series Tricks 2021 to crack questions related to it. On this page, students can also check best Tips & Tricks to Solve Number Series Problems Quickly.

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## Number Series Tricks

What is Number Series?

Number series is a arrangement of numbers in a certain order, where some numbers are wrongly put into the series of numbers and some number is missing in that series, we need to observe and find the accurate number to the series of numbers.

The arrangement of numbers in a certain order, and in which some numbers are placed wrongly in the series and some numbers are missing is called a number series. Based on calculating the addition and subtraction of the numbers, candidates have to observe and find the accurate number to the series of numbers.

Number Series Short Tricks & Methods

There are various tricks to solve the number series problems provided by Mathematics. Check these tricks below –

• If all the numbers are prime, even or odd.
• If all the numbers have a particular divisibility.
• If all the numbers are perfect squares or cubes.
• If all the numbers succeed by a certain number of additions or subtractions or multiplications or divisions, or by adding their cubes and squares.

You Can Check Here: Number Series Question

Types of Questions on Number Series

Here are some of the series patterns which are discussed below:

• Based on subtraction and addition

In the series 4, 9, 14, 19, 24, 29 we can see that it is an increasing series and the rate of increase is 9-4 = 5.

In the series 13, 11, 9, 7, 5 we can see that it is a decreasing series and the rate of decrease is 13-11 = 2

• Based on division and multiplication

In the series 4, 8, 16, 32, 64, we can see that it is an increasing series and the series is increasing by the multiple of 2.

In the series 100, 50, 25, 5, 1 we can see that it is a decreasing series and the series is decreasing as the terms are divided by 5.

• Based On Square And Cube

In the series 8, 27, 125, 343, 1331, 2197, we can see that it is an increasing series. The series is the cube of the consecutive prime numbers from 2 to 13.

Step 4: Check if the series is alternating

For alternating series, candidates need to check whether the series has two different operations, which are being alternately performed, or there is a mix of two series.

Example:

In the series 4, 9 6, 18, 9, 27, 13, 36. This series is a mix of two series 9, 18, 27, 36 and 4, 6, 9, 13.

In the series 200, 600, 1200, 1600, 3200, 3600, 7200 two types of operations are going, one is the addition of 400 and the second is multiplication by 2.

Get Here Important: Mensuration Questions and Answers

Tips For Number Series

• Try to observe if there are any familiar numbers in the given series.
• Familiar numbers are the numbers which are easy to identify like primes numbers, perfect squares, cubes.
• If you are unable to find familiar number, calculate the differences between the numbers and observe the pattern in the differences.
• If the differences are growing slowly it might be an addition or subtraction series or If the differences are growing rapidly it might be a square series, cube series, or multiplicative series.
• If the differences also are not having any pattern then observes every alternate number (ie every 3rd number form a series) for any pattern.
• The possible cases may be like sum or the average of two consecutive numbers gives 3rd number.
• If still you do not find any pattern, it signifies that the series follows a complex pattern. Check for cases like multiplying the number and adding/subtracting a constant number from it to reach the pattern.

Solve Out: Discount Questions and Answers

Types Of Number Series

The most common patterns followed by number series are:

• Series consisting of Perfect Squares:

A series based on Perfect squares is most of the times based on the perfect squares of the numbers in a specific order & generally one of the numbers is missing in this type of series.

Example: 324, 361, 400, 441,?

Sol: 324 = 182 , 361 = 192, 400 = 202, 441 = 212, 484 = 222

• Perfect Cube Series:

It is based on the cubes of numbers in a particular order and one of the  numbers is missing in the series.

Example: 512, 729, 1000,?

Sol: 83, 93, 103, 113

• Geometric Series:

It is based on either descending or ascending order of numbers and each successive number is obtained by dividing or multiplying the previous number by a specific number.

Example: 4, 36, 324, 2916?

Sol: 4 x 9 = 36, 36 x 9 = 324, 324 x 9 = 2916, 2916 x 9 = 26244.

• Arithmetic Series:

It consists of a series in which the next term is obtained by adding/subtracting a constant number to its previous term.

Example: 4, 9, 14, 19, 24, 29, 34 in which the number to be added to get the new number is 5. Now, we get an arithmetic sequence 2,3,4,5.

• Two-stage Type Series:

In a two step Arithmetic series, the differences of consecutive numbers themselves form an arithmetic series.

Example: 1, 3, 6, 10, 15…..

Sol: 3 – 1 = 2, 6 – 3 = 3, 10 – 6 = 4, 15 – 10 = 5….

Now, we get an arithmetic sequence 2, 3, 4, 5

• Mixed Series:

This particular type of series may have more than one pattern arranged in a single series or it may have been created according to any of the unorthodox rules.

Example: 10, 22, 46, 94, 190,?

Sol:

10 x 2 = 20 +2 = 22,

22 x 2 = 44 + 2 = 46,

46 x 2 = 92 + 2 = 94,

94 x 2 = 188 + 2 = 190,

190 x 2 = 380 + 2 = 382.

So the missing number is 382.

Check Out: Problem on HCF and LCM

• Arithmetico –Geometric Series :

As the name suggests, Arithmetico –Geometric series is formed by a peculiar combination of Arithmetic and Geometric series. An important property of Arithmetico- Geometric series is that the differences of consecutive terms are in Geometric Sequence.

Example: 1, 4, 8, 11, 22, 25, ?

Sol: Series Type +3 , X2 ( i.e Arithmetic and Geometric Mixing)

1 + 3 = 4, 4 X 2 = 8, 8 + 3 = 11, 11 X 2 = 22, 22 + 3 = 25, 25 X 2 = 50

Geometrico – Arithmetic Series is the reverse of Arithmetico – Geometric Series. The differences of suggestive terms are in Arithmetic Series.

Example: 1, 2, 6, 36, 44, 440, ?

Sol :Series Type – X 2, + 4, X 6, +8 , X 10

1 X 2 = 2, 2 + 4 = 6, 6 X 6 = 36, 36+ 8 = 44, 44 X 10 = 440, 440 + 12 = 452

• Twin/Alternate Series :

As the name of the series specifies, this type of series may consist of two series combined into a single series. The alternating terms of this series may form an independent series in itself.

Example: 3, 4, 8, 10, 13, 16 ? ?

Sol: As we can see, there are two series formed

Series 1 : 3, 8, 13 with a common difference of 5

Series 2 : 4, 10, 16 with a common difference of 6

So, next two terms of the series should be 18 & 22 respectively.

Know Here: Permutations And Combinations Tricks

Important Points To Remember:

i). If numbers are in ascending order in the number series.

Numbers may be added or multiplied by certain numbers from the first number.

SET – I:

Step 1 : Check whether it is ascending , descending or mixed order.

Step 2 : It is  in ascending order. So add or multiply by certain numbers from the first number.

Step 3 : The difference between first number and second, and difference between second and third and so on., are in increasing order of +4 and +3

Step 4: Hence the answer for above series is 37.

Step 1: Check whether it is ascending , descending or mixed order.

Step 2: It is  in ascending order. So add or multiply by certain numbers from the first number.

Step 3: By adding  first number and second, and  second and third and so on., it is not in the sequence of increasing order. Try multiplication

Step 4: Take 1 and 3, let’s start multiplying 1*3=3, by seeing this we get to know, by multiplying 3*4 it gives 12, and 12*5=60.

Step 4: Hence the answer for above series is 360.

ii). If numbers are in descending order in the number series,

Numbers may be subtracted or divided by certain numbers from the first number.

SET – II :

Step 1 : Find whether the given number is in descending order.

Step 2: It is in descending order . So subtract or divide by certain numbers  from the first number.

Step 3: The difference between first number and second, and difference between second and third and so on, are in order of -16,-8,-4,-2

Step 4: Hence the answer for above series is 3.

Step 1: Check whether it is ascending , descending or mixed order.

Step 2: It is  in descending order. So subtract or divide by certain numbers from the first number.

Step 3: By dividing  first number by 6 it gives 120.

Divide 120/ 5 =24, 24/4=6, 6/3=2, 2/2=1 .It is in decreasing order.

Step 4: Hence the answer for above series is 1.

Check Out: Percentage Tricks

iii). If numbers are in mixing order (increasing and decreasing) in the number series.

Numbers may be in addition, subtraction, multiplication and division in the alternate numbers.

Step 1: Check whether it is ascending , descending or mixed order.

Step 2: It is  in mixing order. So it may be in addition, subtraction, division and multiplication, squares and cubes.

Step 3: In above series it is mixing of square, addition and subtraction.

(14)2= 196+4= 200

(13)2=169. By adding 4 it gives 173. Try subtraction.

169-4=165

Here we found it is in order of squaring a number, adding by 4 and subtracting by 4.

Step 4: Hence the answer for above series is 77.

Step 1: Check whether it is ascending, descending or mixed order.

Step 2: It is in ascending order. So add or multiply by certain numbers from the first number.

Step 3: In above series lets add first number with 3 i.e.,14+3= 17

But with second number we can’t able to add +3 and so on.

Let’s try adding first number and second number i.e. 14+17=31

Second and third, i.e. 17+31 =48 and so on

This series is in the form of miscellaneous

Step 4: Hence the answer for above series is 79.

Note:

We hope that these Number Series Tricks will play an important role in your preparation and save your time. If you have any query or problem related to Number Series Tricks, you can share with us through below given comment box.

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