# How To Solve Number Series Question Quickly

## Solving Number Series Questions Effectively Tips and Tricks

On this page you will find the easiest and most effective way to solve any number series. You never will need any other resource to study.

There are following types of number Series patterns –

2. Alphabet Series (Visit Alphabet Series Page)
3. Alpha Numeric Series(Not asked in Placements, only in CAT exam)

There are the following most popular number series, We will discuss all these in details here we are just introducing them to you, so don’t worry if you don’t see the pattern just yet, after this post you will be able solve any Number Series Question in the world –

### Types of Number Series Problems –

• Add up Series + (13, 18, 23, 28 ….), just adding a constant number everytime.
• Add up Series – (28, 23, 18, 13 ……), just subtracting a constant number every time
• Step up Series (+/-) – 0, 2, 6, 12, 20…. or 20, 12, 6, 2, 0, 0 ….. adding/subtracting a variable number, in this case we are adding 2n for n =0, 1, 2, 3 ……
• Square up (+/-) – 5, 6, 10, 19, 34 …… (adding n2 every time and incrementing value of n starting from 1) or 34, 33, 29, 20, 4 … (Subtracting n2 every time and decrementing value of n =1)
• Square add up Series(+/-) (Will explain this in detail below)
• Cube Up Series
• Prime up (+/-)
• Prime Square up(+/-)
• Arithmetic Series
• Geometric Series

Now lets try to learn each of these in detail, do let us know in comments section if you’re not able to understand any problem concept, we will help you out with alter logic.

• Probability of asking – Very Low
• Difficulty – Low
• Reason – to Introduce Concept

These problems are never asked they are very easy, we are talking about them to introduce the number series from basic.

1. Rule – Just Add a number ‘N’ to the last number.
2. E.g. – 5, (5 + 3 = 8), (8 + 3 = 11), ( 11 + 3= 14) ….
3. Result –  5, 8, 11, 14, 17 ……..

• Probability of asking – Very Low
• Difficulty – Low
• Reason – to Introduce Concept
1. Rule : Just Add a number ‘N’ to the last number.
2. E.g. : 4, (4 – 5 =  (-1)), (-1 -5 = -6), ( -6 – 5 = -11) ….
3. Result : 4, -1, -6, -11, -16 ……..

#### Step Up Series

• Probability of asking – Medium
• Difficulty – Low
• Reason –  Infosys, IBM etc
• After our concept you will always be able to solve this problem and will always look easy, but had you not been reading this 30% students are not able figure out correct series of such problems

Step Up Series +

It is like Add up series, but in Add up a constant number was added, but in step up the number added is not constant​, the following type of additions can be there –

• Ap: + 2, +4, +6
• GP: +3, +6. +12, +24
• Sum of last 2 nos

Example –

Type1(easy to identify) –

1. Rule – Just Add a number ‘aX’ to the last number. i.e 4 +aX = 4 + 1(3) increment value of a: 1, 2, 3, 4…..
2. E.g. – 4, (4 + 1(3) = 7), (7 + 2(3) = 13), ( 13 + 3(3) = 22) ….
3. Result –  4, 7, 13, 22, 34 ……..

Type 2(medium to identify) –

1. Rule – For a number a, multiply with last added number. 6 + a(4) for a = 2.
2. E.g. – 6,
1. ( 6 + 2(4) = 6 + 8 = 14)
2. ( 14 + 2(8) = 14 + 16 = 30)
3. (30 + 2(16) = 30 + 32 = 62)
4. (62 + 2(32) = 62 + 64 = 126)
3. Result –  14, 30, 62, 22, 126 ……..

Type 3(Hard to identify) –

1. Rule – For a number a increment from 1, 2, 3, 4 ….. and multiply with last added number.
2. E.g. – 4
1. 4 + 1(2) = 4 + 2 = 6
2. 6 + 2(2) = 6 + 4 = 10
3. 10 + 3(4) = 10 + 12 = 22
4. 22 + 4(12) = 22 + 48 = 70
3. Result – 6, 10, 22, 70 …..

Step Up Series –

#### Square up and Square Add up Series

• Probability of asking – Medium
• Difficulty – Medium
• Reason –  Infosys, IBM etc
• After our concept you will always be able to solve this problem and will always look easy, but had you not been reading this 50% students are not able figure out correct series of such problems

Square up +(Easy to Identify)

1. Rule – For a number X and for a number a where a = 1, 2, 3….. do next number = x + a2
2. E.g. – 5
1. 5 + 2= 5 + 4 = 9
2. 9 + 32 = 9 + 9 = 18
3. 18 + 42 = 18 + 16 = 34
4. 34 + 52 = 22 + 25 = 77
3. Result – 9, 18, 34, 77 …..

Square up Add up +(Hard to Identify)

1. Rule – For a number X and for a number a where a = 1, 2, 3….. do next number = x + a+ b for b some pattern.
2. E.g. – 5
1. 5 + 2+ 3= 5 + 4 + 3 = 12
2. 12 + 32 + 8(3+5) = 9 + 9 + 8 = 29
3. 29 + 42 +13(8+5) = 29 + 16 + 13 = 58
4. 58 + 52 + 18(13+5) = 58 + 25 + 18 = 101
3. Result – 5, 12, 29, 58, 101 …..

Square up Step up +(Very hard to identify not asked mostly unless paper is very tough)

1. Rule – For a number X and for a number a where a = 1, 2, 3….. do next number = x + a2 + b for b some pattern.
2. E.g. –
1. 5
2. 5 + 22 + 3= 5 + 4 + 3 = 12
3. 12 + 32 + 8(3+5) = 9 + 9 + 8 = 29
4. 29 + 42 +13(8+5) = 29 + 16 + 13 = 58
5. 58 + 52 + 18(13+5) = 58 + 25 + 18 = 101
3. Result – 5, 12, 29, 58, 101 ..

#### Square up and Square Add up Series

• Probability of asking – Low
• Difficulty – Hard
• Reason – Infosys(very rarely) etc
• After our concept you will always be able to solve this problem and will always look easy, but had you not been reading this 90% students are not able figure out correct series of such problems

#### Prime up and Prime Square up Series(Very hard to Identify)

• Probability of asking – Medium
• Difficulty – Hard
• Reason – Infosys, IBM.  etc
• After our concept you will always be able to solve this problem and will always look easy, but had you not been reading this 70% students are not able figure out correct series of such problems

Prime Add up +(Easy to Identify)

1. Rule – For a number X add prime numbers(1, 2, 3, 5, 7, 11, 13, 17, 19 …) iteratively
2. E.g. – 11
1. 11 + 7 = 18
2. 18 + 11 = 29
3. 29 + 13 = 42
4. 42 + 17 = 59
3. Result – 11, 18, 29, 42, 59 ….

Prime Add up -(Easy to Identify)

1. Rule – For a number X add prime numbers(1, 2, 3, 5, 7, 11, 13, 17, 19 …) iteratively
2. E.g. :11
1. 11 – 5 = 6
2. 6 – 7 = -1
3. -1 – 11 = -12
4. -12 – 13 = -25
3. Result – 11, 6, -1, -12, -25 ….

Prime Square up +(Medium to Identify)

1. Rule – For a number X add Squares of prime numbers(12, 22, 32, 52, 72, 112…) iteratively
2. E.g. – 3
1. 3 + 52= 28
2. 28 + 72 = 76
3. 76 + 112 = 197
3. Result – 3, 28, 76, 197 ….

Prime Square up -(Hard to Identify)

1. Rule – For a number X subtract Squares of prime numbers(12, 22, 32, 52, 72, 112…) iteratively

## HOW TO SOLVE NUMBER SERIES-

Number series:

A series of different numbers following some logical pattern of various mathematical concepts. One has to analyze the concept used and accordingly find out the missing number of the series.

Generally, there are 5 different types of series, which are explained below with examples:

## Type 1.Perfect Square questions

### Question 1.

Find the missing numbers from the series?

225, 256, 289, —, 361—, 441

Options:
A.  324, 400
B.  325, 450
C.  320, 392
D.  None of the above

#### Explanation:

(15)2= 15*15= 225

(16)2= 16*16= 256

(17)2= 17*17= 289

(18)2= 18*18= 324

(19)2= 19*19= 361

(20)2= 20*20= 400

(21)2= 21*21= 441

### Question 2.

Find the missing number from the series?

4, 16, 36, –, 100, —, 196

Options:
A.  49, 121
B.  64, 144
C.  81, 169
D.  None of the above

#### Explanation:

Here the series contains a perfect square of ever alternate even number like

2*2= 4

4*4= 16

6*6= 36

8*8= 64

10*10= 100

12*12= 144

### Question 3.

Find the wrong number in the series?

50, 75, 111, 160, 225

Options:
A.  181
B.  224
C.  225
D.  None of the above.

#### Explanation:

Here the first number is 50 which is not a perfect square, the next number is 75, which again is not a perfect square. Hence this is evident that the series is not a perfect square series, but the difference between the two perpetual numbers of the series is 25 (75-50), 36 (111-75), 49 (160-111) and all these numbers are perfect squares, Hence the next number shall be 160+64= 224 But here its 225, Hence Option C is the correct One. ## Type 2. Perfect cube series

Such series consists of numbers that perfect cubes. Some of its examples are mentioned below:

### Question 1.

Fill in the blank with a number that will follow the below-mentioned series?

343, 729, —-, 2197, 3375

Options:
A.  1331
B.  1000
C.  4096
D.  None of the above

#### Explanation:

This series consists of perfect cubes of perpetual odd numbers beginning from 7. Like 7, 9, 11, 13, 15 and so on.

343 (7*7*7)

729 (9*9*9)

1331 (11*11*11)

2197 (13*13*13)

3375 (15*15*15)

### Question 2.

There is one wrong number which is not following the pattern of the series. Find out that number from the options given below?

2197, 5832, 12168, 21952, 35937

Options:

A.  12168
B.  2197
C.  21952
D.  35973

#### Explanation:

133= 2197

183= 5832

233= 12167

283= 21952

333= 35952

In this series 5 is added to each cube digit to get the next cube number. Like (13+5)= 18; (18+5)= 23….

### Question 3.

Find the missing numbers from the series?

9261, 32768,——– , 157464, 274625,———

Options:
A.  79507, 438976
B.  81454, 398676
C.  68921, 45887 6
D.  None of the above.

#### Explanation:

213 = 9261

323 = 32768

433 = 79507

543 = 157464

653 = 274625

763 = 438976

Here 11 is added to each cube digit to get the next cube number like 21+11= 32

31+11= 43 and so on.

## Type 3. Ration Series

This series contains numbers arranged in a particular order, and there is a set pattern of variance between each digit of the series. Now we have to analyze that pattern and accordingly calculate the next missing number of the series.

This is explained with a couple of examples mentioned below:

### Question 1.

Find the missing numbers from the series?

12, 24, —, 96, —, 384

Options:
A.  48, 192
B.  36, 108
C.  72, 288
D.  None of the above.

#### Explanation:

In this series, it is evident that 2 is multiplied to each consecutive number to get the next number. Which is mentioned below:

6*6= 12

112*2= 24

24*2= 48

48*2= 96

96*2= 192

192*2= 384

Therefore option A is the correct one.

### Question 2.

Which one is/are the wrong number which is not following the series trend?

12, 24, 48, 816, 16214, 32424

Options:
A.  16214
B.  12, 24
C.  48, 816
D.  32424

Correct option: A

If we separate each digit of the number:

(1+1= 2; 2+2= 4)= 24

(2+2= 4; 4+4= 8)= 48

(4+4= 8; 8+8= 16)= 816

(81+81= 162; 6+6= 12)= 16212

(162+162= 324; 12+12= 24)= 32424

Hence option A is the correct one.

### Question 3.

Find the missing numbers from the series below?

3, 21, 147, —, 7203, —-

Options:
A.  2209
B.  1029
C.  6172
D.  None of the above

#### Explanation:

This series consists of a sequence where each number is multiplied by 7:

3

3*7= 21

21*7= 147

147*7= 1029

1029*7= 7203

7203*7= 50421

## Type 4. Geometric series

Geometric series is a formula based series wherein the missing number is calculated by either adding, multiplying, subtracting or dividing the consecutive term with a constant number.

Its formula is mentioned below:

G S= {a, ar, ar2, ar3,….}

Where the a= first term of the series

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

### Question 1.

Find the missing numbers from the below-mentioned series?

1, 3, 9, –, 243, —

Options:
A.  81, 729
B.  27, 729
C.  81, 486
D.  None of the above

#### Explanation:

Here a= 1 (first term of the series)

R = 3 ( common number that is multiplied with the consecutive number of the series)

Hence we get:

1

1*3

1*32 = 9

1*33 = 27

1*34 = 81

1*35 = 243

1*36 = 729

### Question 2.

Find the wrong number which does not follow the series pattern?

5, 7, 15, 35, 112, 455

Options:
A.  15
B.  5
C.  7
D. 35
E.  112
F.  455

5*0+7= 7

7*1+7= 14

14*2+7= 35

35*2+7= 112

112*2+7= 231

### Question 3.

Find the missing number from the below series?

9, 81, —, 6561, 59049

Options:
A.  648
B.  729
C.  3281
D.  None of the above

9

9*9= 81

81*9= 729

729*9= 6561

6561*9= 59049

## Type 5. Mixed series

Here the series is formulated by using more than one arithmetic logic.

### Question 1.

Find out the missing numbers from the below series?

81, 80, 84, –, 91, 66, —, 53

Options:
A.)  88, 76
B.)  75, 102
C.)  76, 95
D.)  None of the above

81+ 02= 81

81- 12= 80

80+ 22= 84

84- 32= 75

75+ 42= 91

91- 52= 66

66+ 62= 102

102- 72= 53

### Question 2.

There is one wrong number in the below series which is not following the series pattern. Find out that number?

39, 120, 365, 1092

Options:
A.  39
B.  365
C.  120
D.  1092

12

12*3+3= 39

39*3+3= 120

120*3+3= 363

363*3+3= 1092

### Question 3.

Below series contains a wrong number, find the one which does not follow the series trend?

12, 61, 307, 7656, 38281

Options:
A.  12
B.  307
C.  61
D.  7656
E.  38281

#### Explanation:

12+12*5+1= 61

61*5+1= 306

306*5+1= 1531

1531*5+1= 7656

7656*5+1= 38281

Read Also: Formula for Number Series Question 