# Tips And Tricks And Shortcuts For Number Series

## Number series Tips and Tricks and Shortcuts

Here on this page Number series Tips, Tricks and Shortcuts is given to solve the question easily and effectively. You will also get some of its Types along with question and answers.

## Number Series Tips, Tricks and Shortcuts :

Number Series TypesExplanation
Add up Series (+)Just adding a constant number everytime. For example: (13, 18, 23, 28 ….).
Add up Series (- ) Just subtracting a constant number every time. For example : (28, 23, 18, 13 ……).
Step up Series (+/-)Adding/Subtracting a variable number, in this case we are adding 2n for n = 0, 1, 2, 3 …… For example : 0, 2, 6, 12, 20…. or 20, 12, 6, 2, 0, 0 …..
Square up (+/-)Given series is in the square of n where n= 1,2,3,4,5,6… i.e. 1,4,9,16,25,36…
Square add up Series(+/-)Adding n2 every time and incrementing value of n starting from 1 i.e. 1,5, 14, 30, 55, …… and Subtracting n2 every time and decrementing value of n i.e. 34, 33, 29, 20,
Cube Up Series :Given series is in the cube of n where n = 1,2,3,4,5,6… i.e. 1,8,27,64,125,216….
Cube add up Series : Adding $n^{3}$ every time with incrementing of n by 1 i.e. 1,9,36…
Prime up(+/-) :+Sequence consist of Prime numbers i.e. 2,3,5,7,11…
Prime Square up(+/-) : Sequence consist of squares of prime numbers i.e. 4,9,25,49,121..
Arithmetic Series:Sequence consist of Arithmetic Progression i.e. 3,6,9,…
Geometric Series :Sequence consist of Geometric Progression i.e. 2,6,18,54,…

### Tips and Tricks – Perfect Square Series

Consists of the perfect square of some numbers arranged in a specific order, with one number missing. Now we’ve to find the pattern the series is following and fill up the blank accordingly by finding that number.

Question 1. 100,121,144,__, 196

Solution:

This series consists of a perfect square of consecutive numbers 10, 11, 12, 13

Hence 169 will come in the blank.

### Tips and Tricks – Perfect Cube Series

It consists of a cube of numbers sequenced in a particular order. The sequence would be like go om adding the cube of that specific given number.

Question 2. 9,64, 125, __, 343

Solution:

This series consists of a series of numbers with perfect cubes the is (3 x 3 x 3), (4 x 4 x 4), (5 x 5 x 5), (6 x 6 x 6), (7 x 7 x 7)

Hence 216 will be coming in the blank, as the series is following a trend of cubes of numbers in sequential order.

### Tips and Tricks and Shortcuts- Ration Series

This type of series consists of numbers arranged in sequential order (following a particular trend, i.e., Either increasing or decreasing). Now, all we have to do here is to trace out this trend,(which could be *, /, +, -) of each number of the series with a fixed number) by finding the proportional difference between the numbers of the series.

Question 3. 3, 6, 9, 12, __, 18, 21

Solution:

Here the series is following an increasing trend in which three is added to each number of the series.

3

6 (3+3)

9 (6+3)

12 (9+3)

15 (12+3)

18 (15+3)

21 (18+3)

### Tips and Tricks and Shortcuts – Arithmetic series

In this kind of sequences, each number is found by ( + , -) each term by a constant number.

The formula of  A S = {a, a+d, a +2d.….}

Where a= first term of the series

d = common difference

Question 4. 3, 6, 9 , 12

Solution:

Here a = 3(first term of the series)

d = 3

Hence we get:

3 + 3 = 6

6 + 3 = 9

9 + 3 = 12

12 + 3 = 15

### Tips and Tricks and Shortcuts – Geometric series

In this kind of sequences, each number is found by (*, /) each term by a constant number.

The formula of G S= {a, ar, ar2, ar3,….}

Where a= first term of the series

R= factor or difference between the term, also known as the common ratio.

Question 5. 1, 2, 4, 8, 16, 32

Solution:

Here a = 1 (first term of the series)

r = 2 (a standard number that is multiplied with the consecutive number of the series)

Hence we get:

1

1 x 2

1 x 22

1 x 23, ….)

### Tips and Tricks and Shortcuts – Mixed series

In such series, while calculating the difference, there can be two steps involved in getting the next consecutive number of the series. So we’ve to follow the same pattern to get the perpetual number of the series.

Question 6. $1, \frac{5}{2}, \frac{10}{3}, \frac{17}{4}, —$

Options:

A.  $\frac{26}{5}$

B.  $\frac{24}{5}$

C.  $\frac{21}{5}$

D.  5

Correct Option: A

Explanation:

Here we’ve to observe the trend that this series is following, as each term is divided by a specific number, i.e., 1 then 2 then3 then 4 and so on. Hence we can make out that the denominator must be 5.

Now comes the numerator, where the 1’st number is 1.

Then comes 5, now how can we get 5 from the term number 2. It can come by $\frac{2^{2} + 1 }{2} = \frac{5}{2}$ Next comes $\frac{3^{2} + 1 }{3} = \frac{10}{3}$,$\frac{4^{2} + 1 }{4} = \frac{17}{4}$, $\frac{5^{2} + 1 }{5} = \frac{26}{5}$

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### 7 comments on “Tips And Tricks And Shortcuts For Number Series”

• pratip109

In Perfect Cube Series- Q1.) 9,64, 125, __, 343
9 is not a perfect cube. Its a square of 3. The pattern should be 27, 64, 125, ___, 343

• Rupa

hi sir/mam…..
this tips are very useful to every one and me also, iam following to learn and improve my aptitude sir/mam
we want so many tips of apptitude to develope our speed to solve
thank you so much sir/mam

• Savitri

solving tricks is very super Sir

• HelpPrepInsta

Thank you for your appreciation and also we want you to know that we are more than happy to help you and serve you better!!!

• Shweta

Tysm for the tips😍

• Vanitha B Mulimani

the explanation for the mixed series is not appropriate
when we solve for (4^2+1)/2 for 4 condition its will be 17/4 not 15/4

• Nishu Sagar

@Vanitha B Mulimani
thank you for your feedback. We have resolve the issue.