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**Introduction**

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.

The sequenceis the list of numbers written in a specific order.

**Example:** 1, 4, 9, 16, 25, 36....

**Some Common Types and Their Tricks**

**➢ Type 1 - Addition / Subtraction or Multiplication / Division**

**Example**** 1: 19, 23, 39, 75, _, 239**

- The most common trick to solve a number series is to solve by checking the difference between two adjacent numbers, but the 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 assume with the help of the difference between the first and last number of the given sequence.
- If the difference seems to be less according to the number of steps used to make the last number from first than we should check addition.
- If the difference seems to be large or too large one must check the multiplication trick between the adjacent numbers.

In Example 1, given above, the 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 the number of steps required to start from the first number till the last number.
**In Example 1**, 19 becomes 239 in five steps, because there are four more numbers between them, one of which we have to find out.- The 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.

Question 1:Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?

**Example 2: 10, 31, 95, 288, ___, 2609**

As we can see in the above example, the difference between the first number (10) and the last number (2609) is 2599 in five steps, which indicate us to check multiplication trick between the numbers.

(288*3) + 4 = 868, is the correct answer.

Note :While checking multiplication trick always start from right end of the sequence.

**Example 3:**** 30, 34, 43, 59, 84, 120,?****(a) 169****(b) 148****(c) 153****(d) 176****(e) None of these****Ans. (a)****Solution: **__The given pattern is:__

+4, +9, +16, +25 and so on.

So, missing term is 169 = 120 + 49

**Example 4:** **40, 54, 82, ?, 180, 250****(a) 142****(b) 124****(c) 136****(d) 163****(e) None of these****Ans. (b)****Solution: **

The pattern is: +14, + 28, + 42, + 52, + 70

So, missing term is 82 + 42 = 124

Question 2:Look carefully for the pattern, and then choose which pair of numbers comes next - 8,11, 21, 15, 18, 21, 22

**Example 5:**** 0, 1, 3, 8, 18, 35, 264(a) 62(b) 35(c) 18(d) 8(e) None of these**

So, 264 is wrong and must be replaced by 35 + (5

**Example 6:**** 1, 9, 125, 49, 729, 121, 2147(a) 2147(b) 729(c) 125(d) 1(e) None of these**

**Example 7:**** 5531, 5506, 5425, 5304, 5135, 4910, 4621****(a) 5531****(b) 5425****(c) 4621****(d) 5135****(e) 5506****Ans. (a)****Solution: **The number should be 5555 in place of 5531.

-72, -92, -112, -132, -152, -172…

**Example 8: ****6, 7, 9, 13, 26, 37, 69****(a) 7****(b) 26****(c) 69****(d) 37****(e) 9****Ans. (b)****Solution: **The number should be 21 in place of 26.

The pattern is: +1, +2, +4, +8, +16, +32

**Example 9:**** 1, 3, 10, 36, 152, 760, 4632****(a) 3****(b) 36****(c) 4632****(d) 760****(e) 152****Ans. (d)****Solution: **The number should be 770 in place of 760.

The pattern is: ×1 +2, ×2 +4, ×3 +6, ×4 + 8, ×5 +10, ×6 + 12, …

**Example 10:**** 4, 3, 9, 34, 96, 219, 435(a) 4(b) 9(c) 34(d) 435(e) 219**

Hence, 435 should be replaced with 433

**Example 11:**** 157.5, 45, 15, 6, 3, 2, 1****(a) 1****(b) 2****(c) 6****(d) 157.5****(e) 45****Ans. (a)****Solution: **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.

**(a) Perfect Square Series: **This type of series is based on the **square** of a number that is in the same order and one square number is missing in that given series.

Question 3:In the following options, a few number series are present. One of them has an error, pick the wrong one out:

**Example 1:** 841, ?, 2401, 3481, 4761**Answer:** 29^{2}, 39^{2}, 49^{2}, 59^{2}, 69^{2 }

Question 4: In the sequence given below, a term is missing. The missing term is written in the options that are present below. Find the missing term and choose it from the options below: 8, 12, 21, 37, __

**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}**(b) Perfect Cube Series: **This type of series is based on the **cube** of a number that is in the 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 }

Question 5:In the following series, a number is such that it does not belong to the arrangement.

8000, 27000, 64000, 105000

Select the option that has this number:

8000, 27000, 64000, 105000

Select the option that has this number:

**➢ **

- 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: 6, 15, 35, 77, 143, __.**

In the above example, all the previous tricks are not applicable to get an 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.

Question 6:Next number in series 31, 41, 47, 59, __?

**➢ **

- A series in which a number is made by using previous two numbers are called Fibonacci series.

**Example****: 1, 4, 5, 9, 14, 23, ___**

In the above sequence, all the numbers are the sum of the previous two numbers.

Therefore, 23+14 = 37, is the correct answer.

**➢ **

**Example 1:**

In the above sequence, the difference between two numbers is the sum of the 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.

**➢ **

- When numbers given as a hint in a question are more or when a question asks two numbers of a series or the same number come twice in a series, these all give a 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

Question 7:In the given series, a number is missing. The same number is present in the options below.

32, 40, 24, 16, 24, __

Select the missing number.

32, 40, 24, 16, 24, __

Select the missing number.

**➢ **

When the numbers of the sequence are given in the decimal form is decimal pattern series.**Example 1:**** **

So, the answer is 18 * 0.8 = 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

**➢ **

While using bracket pattern we multiply first outside and either add or sub based on given number.

**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

**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

**➢ **

**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

(19-6)*1=13

(13-5)*2=16

(16-4)*3=36

**➢ **

This is the latest pattern question asked in latest exams.

**Example 1:**** ****Ans.** 33

**Example 2:**** ****Ans.** 606 + 721 = 1327

Question 8:In the given series, only one number is wrong.

3, 9, 19, 32

Find out the wrong number.

3, 9, 19, 32

Find out the wrong number.

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