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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, 36â€¦â€¦..**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**

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

(1) 2147

(2) 729

(3) 125

(4) 1

(5) None of these

The number should be 5555 in place of 5531.

-72, -92, -112, -132, -152, -172â€¦

**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.

Ã—1 +2, Ã—2 +4, Ã—3 +6, Ã—4 + 8, Ã—5 +10, Ã—6 + 12, â€¦**Example 10:**** 4, 3, 9, 34, 96, 219, 435(1) 4(2) 9(3) 34(4) 435(5) 219**

The series is 02+ 4, 12+2, 32+0, 62-2, 102-4, 152- 6,212 â€“ 8â€¦

Hence, 435 should be replaced with 433

The number should be 2 in place of 1.

3.5, 3, 2.5, 2, 1.5, 1, .

**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 :** 29^{2}, 39^{2}, 49^{2}, 59^{2}, 69^{2}

**Example 2:** 1, 9, 25, ?, 81, 121**Answer :**** **1^{2}, 3^{2}, 5^{2}, 7^{2}, 9^{2}, 11^{2}

**Example 3:** 289, 225, 169, ?, 81**Answer:** 17^{2}, 15^{2}, 13^{2}, 11^{2}, 9^{2}**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 :** 15^{3}, 22^{3}, 29^{3}, 36^{3}, 43^{3}

(Each cube digit added with seven to become next cube number)

**Example 2:** 729, 6859, 24389, ?, 117649, 205379**Answer :** 9^{3}, 19^{3}, 29^{3}, 39^{3}, 49^{3}, 59^{3}

**Example 3:** 1000, 8000, 27000, 64000, ?**Answer:** 10^{3}, 20^{3}, 30^{3}, 40^{3}, 50^{3}**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: â€“ 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

**T****ype 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 â€“ 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 â€“ 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 â€“** 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 â€“** 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 â€“** 36**TYPE 10 - FACTORIAL BASED SERIS**

This is latest pattern question asked in latest exams**Example 1:**** ****Ans â€“** 33**Example 2:**** ****Ans -** 606+721=1327

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