# Number Series Tricks & Tips

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__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.

In competitive exams number series are given and where you need to find missing numbers. The number series are come in different types. At first you have to decided what type of series are given in papers then according with this you have to use shortcut tricks as fast as you can .

Generally, two kinds of series are asked in the examination. One is based on numbers and the other based on alphabets**.
**

**Step 1:**Observer are there any familier numbers in the given series. Familier numbers are primes numbers, perfect squares, cubes … which are easy to identify.

**Step 2:**Calculate the differences between the numbers. Observe the pattern in the differences. If the differences are growing rapidly it might be a square series, cube series, or multiplicative series. If the numbers are growing slowly it is an addition or substration series.

If the differences are not having any pattern then

1. It might be a double or triple series. Here every alternate number or every 3rd number form a series

2. It might be a sum or average series. Here sum of two consecutive numbers gives 3rd number. or average of first two numbers give next number

**Step 3:** Sometimes number will be multiplied and will be added another number So we need to check those patterns.

__Different types of Number series:__

** 1) Integer Number Sequences**– There are particular formulas tricks to solve number series. Each number series question is solved in a particular manner. This series is the sequence of real numbers decimals and fractions. Number series example of this is like 1, 3, 5, 9….. etc. in which what should come next is Solved by number series shortcuts tricks performed by the candidate.

** 2) Rational Number Sequences**– These are the numbers which can be written as a fraction or quotient where numerator and denominator both consist of integers. An example of this series is ½, ¾, 1.75 and 3.25.

** 3) Arithmetic Sequences –** It is a mathematical sequence which consisting of a sequence in which the next term originates by adding a constant to its predecessor. It is solved by a particular formula given by the mathematics Xn = x1 + (n – 1)d. An example of this series is 3, 8, 13, 18, 23, 28, 33, 38, in which number 5 is added to its next number.

** 4) Geometric Sequences** – It is a sequence consisting of a multiplying so as to group in which the following term starts the predecessor with a constant. The formula for this series is Xn= x1 r n-1. An example of this type of number sequence could be the following:

2, 4, 8, 16, 32, 64, 128, 256, in which multiples of 2 are there.

** 5) Square Numbers** – These are also known as perfect squares in which an integer is the product of that integer with itself. Formula= Xn= n. An example of this type of number sequence could be the following:

1, 4, 9, 16, 25, 36, 49, 64, 81, ..

** 6) Cube Numbers** – Same as square numbers but in these types of series an integer is the product of that integer by multiplying 3 times. Formula= Xn=n^3. Example:-1, 8, 27, 64, 125, 216, 343, 512, 729, …

** 7) Fibonacci Series** – A sequence consisting of a sequence in which the next term originates by addition of the previous two

Formula = F0 = 0, F1 = 1

Fn = Fn-1 + Fn-2. An example of this type of number sequence could be the following:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

__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.

**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

**1. Pure Series**

**2. Difference Series**

**3. Ratio Series**

**4. Mixed Series**

**5. Geometric Series**

**6. Two-tier Arithmetic Series**

**7. Other Type**

**Some Examples ;**

**YOU MUST LEARN SQUARES OF NUMBERS UPTO 40 AND CUBES OF NUMBERS UPTO 20.**

Note: In the wrong number series, the pattern of series will always be wrong immediately before and after of the wrong number.

There are uncountable numbers of series because series is an imagination. Some of the important series pattern are discussed below:

**1. Based on addition and subtraction.**

4,9,14,18,24,29

the difference of two successive numbers is 5 but difference of 18 and 14 is 4, difference of 24 and 18 is 6. So, wrong number is 18. Correct answer is 19.

**2. Based on multiplication and division.**

18,28,40.5,60.75,91.125,136.6875

Solution: Problem with this type of series is how to identify these types of series. Check the difference between successive numbers.

—-10—-12.5—-20.25—-30.375—-45.5625

we can see that the difference is half of the previous number. 10 is not the half of 18 and 12.5 is not the half of 28. So, 28 is wrong and correct number is 27.

**3. Based on square and cube.**

8 27 125 512 1331 2197

Solution: 2^{3}=8, 3^{3}=27, 5^{3}=125, 8^{3}=512,11^{3}=1331,13^{3}=2197

In this all are cubes of number 2,3,5,8,11,13. These numbers are prime numbers except 8 and from 2 to 11, 7 is also prime number which is missing. In place of 8^{3}, there should be 7^{3} i.e. 343

**4. Based on mix pattern.**

6,11,21,40,81,161

This series could have followed two patterns.

**Pattern 1:** difference is –5—10—-19—–41—80. Successive difference is2 times of previous one. But 19 and 41 is not following the pattern. We can guess that something is wrong in this term if we want 20 and 40, we have to replace 40 by 41. Hence 40 is wrong.

**Pattern 2:** 6

6×2-1 = 11

11×2-1 = 21

21×2 -1 = 41

41×2 – 1 = 81

81×2 -1 = 161 Hence, 40 is wrong

If you go through various types of pattern of wrong number series and have practiced them. You will not have any problem in solving the series. Now, we will discuss previous year asked questions based on number series.

**Example 1:** 12 12 18 45 180 1080 12285

In this series also there can be two pattern.

Pattern 1 |
Pattern 2 |

12×1 = 12 12x(1.5) = 18 18x(1.5 +1) = 45 45x(2.5+1.5) = 180 180x(4+2.5)= 1170 1170x(6.5+4) = 12285 |
12x(1+0) = 12
12x(1+.5) = 18 18x(1.5+1) = 45 45x (2.5+1.5) = 180 1080x(6+2.5) = 9180 |

**So,If it follows pattern1, the wrong number in series is 1080 and if it follows pattern2, the wrong number in series is 12285. It depends on options given in exams**.

**Example 2**: 7 5 7 17 63 ? (SBI PO Prelims 2016)

**Answer:** 309

7×1 – 2 = 5

5×2 – 3 = 7

7×3 – 4 = 17

17×4 – 5 = 63

63×5 – 6 = 309

**Example 3:** 50…… 61 89 154 280 (SBI PO Prelims 2016)

**Answer :** 52

50+(1^{3}+1) = 52

52+(2^{3}+1) = 61

61+(3^{3}+1) = 89

89+(4^{3}+1) = 154

154+(5^{3}+1) = 280

**Example 4**: 17, 19, 25, 37, ……,87 (SBI PO Prelims 2016)

**Answer**: 57

17 + 1 x 2 = 19

19 + 2 x 3 = 25

25 + 3 x 4 = 37

37 + 4 x 5 = 57

57 + 5 x 6 = 87

**Example 5**: 11, 14, 19, 28, 43, ? (SBI PO Prelims 2016)

**Answer**: 66

3…5…9…15…23

2…4….6…….8

Answer 43+23= 66

**Example 6:** 26 144 590 1164 ? (SBI PO Prelims 2016)

**Answer**: 1182

26 x 6 – 12 = 144

144 x 4 + 14 = 590

590 x 2 – 16 = 1164

1164 x 1 + 18 = 1182

**Example 7**: 6 48 8 70 9 63 7 Find the wrong number?

**Answer:** 9×7=63, 9×8=72,8×6=48

So, 70 is wrong in this series

**Example 8:** 1,4,11,34,102,304,911

**Answer:** 102

Pattern of Series is

1

1×3+1 = 4

4×3-1 = 11

11×3+1 = 34

34×3-1 = 101

101×3+1 = 304

304×3-1 = 911

**Example 9**: 1,2,12,146,2880,86400,3628800

**Answer**: 146

1

1x1x2=2

2x2x3=12

12x3x4=144

144x4x5=2880

2880x5x6=86400

86400x6x7= 3628800

**Example 10:** 0,6,23,56,108,184,279

**Answer:** 108

1^{3}-2^{0} = 1-1 =0

2^{3}-2^{1 }= 8-2 =6

3^{3}-2^{2 }= 27-4 = 23

4^{3}-2^{3}= 64-8 = 56

5^{3}-2^{4}= 125-16 = 109

6^{3}-2^{5}= 216-32 = 184

7^{3}-2^{6}= 343-64 =279

**Example 11**: 813,724,635,546,457,564,279

**Answer **: 564

Hundred place digit is decreasing by 1, tens place is increasing by 1 and unit place digit is also increasing by 1. But this pattern is not followed in 564. 368 should be there in place of 564.

**Example 12**: 0,4,19,48,100,180,294

**Answer:** 19

1^{3}-1^{2}=0

2^{3}-2^{2 }= 4

3^{3}-3^{2 }= 18

4^{3}-4^{2}= 48

5^{3}-5^{2}=100

6^{3}-6^{2}= 180

7^{3}-7^{2}=294

**Example 13:** 3.2, 4.8, 2.4, 3.6, 1.6, 2.7

**Answer :** 1.6

3.2 x 1.5 = 4.8

4.8 ÷ 2 = 2.4

2.4 × 1.5 = 3.6

3.6 ÷ 2 = 1.8

1.8 x 1.5 = 2.4

**Example 14:** 2, 9,24,55,117,245

**Answer** : 117

2×2+5 = 9

9×2+6 = 24

24×2+7 = 55

55×2+8 = 118

118×2+9 = 245

**Example 15:** 109,131,209,271,341,419

**Answer**: 131

11^{2}-12 = 109

13^{2}-14 = 155

15^{2}-16 = 209

17^{2}-18 = 271

19^{2}-20 = 341

21^{2}-22 = 419

**Example 16:** 6, 7,27, 115,513,3069

**Answer **: 115

6×2-5 = 7

7×3+6 = 27

27×4-7 = 101

101×5+8 = 513

513×6-9 = 3069

- Prime number Series :

**Example** (1) : 2,3,5,7,11,13, ………..** **

**Answer** : The given series is prime number series . The next prime number is 17.** **

**Example** (2) :2,5,11,17,23,………..41.** **

**Answer**: The prime numbers are written alternately.

- Difference Series :

**Example **(1): 2,5,8,11,14,17,………..,23.** **

**Answer**: The difference between the numbers is 3. (17+3 = 20)** **

**Example** (2): 45,38,31,24,17,………..,3.

**Answer**: The difference between the numbers is 7. (17-7=10). III. Multiplication Series:

**Example **(1) : 2,6,18,54,162,………,1458.

**Answer**: The numbers are multiplied by 3 to get next number. (162×3 = 486).** **

**Example**: (2) : 3,12,48,192,…………,3072.** **

**Answer** : The numbers are multiplied by 4 to get the next number. (192×4 =768).

- Division Series:

**Example**(1): 720, 120, 24, ………,2,1

**Answer**: 720/6=120, 120/5=24, 24/4=6, 6/3=2, 2/2=1.** **

**Example** (2) : 32, 48, 72, 108, ………., 243.** **

**Answer**: 2. Number x 3/2= next number. 32×3/2=48, 48×3/2=72, 72×3/2=108,108×3/2=162.

- n
^{2}Series:

**Example**(1) : 1, 4, 9, 16, 25, ……., 49** **

**Answer**: The series is 12, 22, 32, 42, 52, …. The next number is 62=36;** **

**Example** (2) : 0, 4, 16, 36, 64, …….. 144.** **

**Answer** :The series is 02, 22, 42, 62, etc. The next number is 102=100.

- n
^{2}−1Series :

**Example** : 0, 3, 8, 15, 24,35, 48, ……….,** **

**Answer** : The series is 12-1, 22-1, 32-1 etc. The next number is 82-1=63.

Another logic : Difference between numbers is 3, 5, 7, 9, 11, 13 etc. The next number is (48+15=63).

VII.n^{2}+1 Series : ** **

**Example** : 2, 5, 10, 17, 26, 37, ………., 65.** **

**Answer** : The series is 12+1, 22+1, 32+1 etc. The next number is 72+1=50.

VIII. n^{2}+n Series (or) n^{2}−n Series :

**Example** : 2, 6, 12, 20, …………, 42.** **

**Answer** : The series is 12+1, 22+2, 32+3, 42+4 etc. The next number = 52+5=30.

Another Logic : The series is 1×2, 2×3, 3×4, 4×5, The next number is 5×6=30.

Another Logic : The series is 22-2, 32-3, 42-4, 52-5, The next number is 62-6=30.

IX. n^{3} Series :** **

**Example** : 1, 8, 27, 64, 125, 216, ……… .** **

**Answer** : The series is 13, 23, 33, etc. The missing number is 73=343.

X. n^{3}+n Series :

**Example** : 2, 9, 28, 65, 126, 217, 344, ………..** **

**Answer** : The series is 13+1, 23+1, 33+1, etc. The missing number is 83+1=513.

- n
^{3}−1Series :

**Example** : 0, 7, 26, 63, 124, …………, 342.** **

**Answer**: The series is 13-1, 23-1, 33-1 etc The missing number is 63-1=215.

XII. n^{3}+n Series :** **

**Example** : 2, 10, 30, 68, 130, ………….., 350.** **

**Answer** : The series is 13+1, 23+2, 33+3 etc The missing number is 63+6=222.

XIII. n^{3}−n Series :** **

**Example** :0, 6, 24, 60, 120, 210, ………….., ** **

**Answer** : The series is 13-1, 23-2, 33-3, etc. The missing number is 73-7=336.

Another Logic : The series is 0x1x2, 1x2x3, 2x3x4, etc. The missing number is 6x7x8=336.

XIV. n^{3}+n^{2} Series :** **

**Example** : 2, 12, 36, 80, 150, …………, ** **

**Answer**: The series is 13+12,23+22,33+32etc. The missing number is 63+62=252

- n
^{3}−n^{2}Series:

** Example**: 0,4,18,48,100,……………..,

**Answer** : The series is 13-12,23-22,33-32 etc. The missing number is 63-62=180

XVI. xy, x+y Series:

**Example**: 48,12,76,13,54,9,32,……………,

**Answer **:2. 4+8=12, 7+6=13, 5+4=9 .: 3+2=5.

Some steps which may be helpful to solve number series.

Step 1: Check difference

Step 2: If step 1 does not work, then check difference of difference. If it also does not work, try to find is there any multiplication or division relationship between numbers?

Step 3: If difference is sharply increasing or decreasing, then you can guess that it may be due to multiplication or division pattern of series.

Step 4: If there is more irregularity in difference, then it may be combination of above discuss steps.

Step 5: If none of the steps works, then try to use elimination method, which may help you in eliminating 2 to 3 options.

**Tricks to solve Number Series With Detailed Examples**

Below are the common pattern of questions usually asked in numbers series:

**I. Fibonnaci Series**

The Fibonnaci sequence is a series of numbers where a no. is found by adding up the nos. before it. Let us understand the series with the help of an example:

**Example 1:**

**0,1,1,2,3,5,8,13,21,___.**

**Example 2:**

**20, 12, 32, 44, 76, 120,____.**

**II. Addition series**

There can be 2 types of pattern in addition series.

**(A) Same number Addition series**

In this type of series, the difference between 2 consecutive elements is same i.e. same digit is to be added to the previous element to obtain the next element.

**Example 3:**

**3, 6, 9, 15, 18,___.**

Sol. In the given series, the difference between the two consecutive elements is same i.e 3.

In this type of series, the number added to each term is in increasing order.

**(B) ****Increasing order Addition series**

In the given series, the difference between 2 consecutive numbers is in increasing order.

**Example 4:**

**2, 5, 9, 14, 20, 27,____.**

**Sol. **In the given series, the difference between 2 consecutive numbers is in increasing order i.e 3,4,5,6,7 and 8 respectively.

**III. Subtraction series**

**(A) Same Number Subtraction Series**

In this type of series, each time the same number is subtracted from the previous element to obtain the next element.

**Example 5:**

**52, 49, 46, 43, 40,____.**

**Sol.** Here the difference between 2 consecutive nos. is 3.

**(B) Increasing order Subtraction Series**

**Example 6:**

**94, 90, 85, 79, 72, 64,___.**

**Sol**. Here the difference between 2 consecutive elements is in increasing order.

**IV. Multiplication Series**

**(A) Same number multiplication Series**

In this series, the ratio between 2 consecutive elements is same.

**Example 7:**

**4, 12, 36, 108, 324,____.**

In the given series, previous element is multiplied by 3 to obtain the next element and therefore the ratio between 2 consecutive elements is same.

**(B) Increasing order of Multiplication Series**

In this type of series, elements are multiplied in increasing order to find the next element.

**Example 8:**

**5, 5, 7.5, 15,___.**

In the given series, the ratio between 2 consecutive elements is in increasing order and elements are multiplied by the numbers in increasing order.

**V. Division series**

**(A) Same number division series**

In this type, each time the previous element is divided by same digit to obtain the next element.

**Example 9:**

**1600, 400, 100, 25,___.**

**Sol.** In the given series, previous element is divided by 4 to get the next element.

1600/4 = 400

400/4 = 100

100/4 = 25

25 /4 = 6.25

Therefore, the correct answer = 6.25

**(B) Increasing/Decreasing order division series**

**Example 10:**

**46080, 3840, 384, 48, 8, 2,____.**

**Sol. **In the given series, elements are divided by 12, 10, 8, 6 and 4 respectively to obtain the next elements.

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**VI. Addition & Multiplication together**

**Example 11:**

**1, 3, 7, 15, 31,____.**

**Sol. **In such a series , addition and multiplication is used together.

**Example 12:**

**5, 6, 14, 45, 184,____.**

**Sol. **In this series, the previous elements are multiplied respectively by numbers in increasing order & numbers in increasing order respectively added in such multiplication to obtain the next element.

**VII. Decimal Fraction**

**Example 13:**

**36, 18, 18, 27, 54,___.**

**Sol.** In this series, following pattern is used:

**VIII. Difference of difference series**

Calculate the differences between the numbers given in the series provided in the question. Then try to observe the pattern in the new set of numbers that you have obtained after taking out the difference.

**Example 14:**

**1, 3, 8, 19, 39, 71,_____.**

**Sol. **The following pattern is observed in the given series

**IX. Twin series**

In this type of series, odd place element males one series while the even place elements make another series.

**Example 15:**

**3, 6, 6, 12, 9, 18,______.**

**Sol. **In this series, following pattern is used:

**X. Tri-series**

**Example 16:**

**2, 9, 23, 3, 8, 25, 4,_____.**

**Sol.** Following pattern is used in the given series

**XI. Square series & Cube series**

**Example 17:**

**4, 9, 16, 25, 36, 49,____.**

**Sol.** In the given series, the following pattern is used

**2 ^{2}, 3^{2}, 4^{2}, 5^{2}, 6^{2}, 7^{2}, 8^{2}**

**Example 18:**

**Sol.** In the given series, the following pattern is used

**1 ^{3}, 2^{3}, 3^{3}, 4^{3}, 5^{3}, 6^{3}**

**XII. Square & Cube addition**

**Example 19:**

**2, 3, 7, 16,_____.**

**Sol.** In the given series, the following pattern is used

**Example 20:**

**1, 2, 10, 37,____.**

**Sol.** In the given series, the following pattern is used

**XIII. Digital Operation of Numbers**

In this type of series, the digits of each number are operated in a certain way to obtain the next element of the series.

**Example 21:**

**94, 36, 18,_____.**

**Sol.** In the given series, the following pattern is used

9 *4 = 36

3 * 6 = 18

1 * 8 = 8

**Correct answer – 8**

**23, 26, 24, 27, 25, 28, ?**In this problem, numbers are increasing and decreasing and the variations are also small, therefore both addition and subtraction operations can take place.

23+3=26

26-2=24

24+3=27

27-2=25

25+3=28

28-2=26

**Difficulty level : hard**

(there is no need to by heart all this pattern , just know how the patterns can be in the series this will make easy to guess the pattern for you)

For series

**a, b, c, d, e, f,**the pattern will be any one of these following patterns.

- a) If the resultant number is greater than the last number then it will be the addition or subtraction of square/cube of number i.e. pattern(I).
- b) If the resultant number is less than the last number and difference is large, then the pattern will be any of these (II) or (III) or (IV) or (V)
- c) If the resultant number is less than the last number but difference is small it belongs to (VI).

**Example 1: 3, 732, 1244, 1587, 1803, 1928, ?**

**Step 1: **1803*2 = 3606 >1928 therefore it will be pattern (I)

**Step 2: **Now find the difference between the two numbers consecutively

**Example 2: 13, 25, 61, 121, 205, ?**

**Step 1: **121*2>205 and variation is small , so it will follow pattern (I)

**Step 2: **Difference between 13 & 25 = 12

difference between 25 & 61 = 36 (12*3)

difference between 61 & 121 = 60 (12*5)

difference between 121 & 205 = 84 (12*7)

Obviously next number in series will be addition of 108(12*9) with 205 = 313

**Example 3: 1, 6, 36, 240, 1960, ?**

**Step 1: **240*2<1960 and the variation is large too, so the pattern will be either (II) or (III) or (IV) or (V)

**Step 2: **Now use the trial and error method but don’t apply it to whole series use it in any of the two numbers.

1*2 + 2*2 = 6

6*4+3*4=36

36*6+4*6=240

240*8 +5*8 =1960 so 1960*10+6*10=19660

__Example 4:__ 13, 14, 30, 93, 376, 1885, ?

**Step 1.**376*2<1885 and the variation is also large, so the pattern will be (II) or (III) or (IV) or (V)

**Step 2.**Use the trial and error method and find the pattern, it is wise to check in last two numbers.376*5=1880 adding 5 we get correct number 1885So pattern is 376*5+5=188513*1+1=14

14*2+2=30

Answer will be 1885*6+6=11316

**Example 5: 12, 35, 81, 173, 357, ?**

**Step 1.** 173*2<357 and the variation is small so it will follow pattern (VI).

**Step 2.** 173*2=346 to get 357 add 11 .

**Pattern is **

173*2+11=357

12*2+11=35

Answer will be 357*2+11=725

**Miscellaneous**

Number series is a vast topic , there always an exception cases .)

**Example : 7, 4, 5, 9, ? , 52.5, 160.5**

If the numbers in the series are increasing and decreasing and a decimal numbers are in the series then you can guess decimal numbers playing in this series

7*0.5 + 0.5 = 4

4*1+1=5

5*1.5+1.5 = 9

9*2+2 = 20

20*2.5+2.5 =52.5

**Example: 120 15 105 17.5 87.5 ?**

120÷8 =15

15*7=105

105÷6=17.5

17.5*5=87.5

87.5÷4=21.875

**Example: 3 6 21 28 55 66 ? 120**

Difference between 3&6 is 3

Difference between 21&28 is 7

Difference between 55& 66 is 11

Difference between ? & 120 is 15 therefore the number is 105

- Try to observe if there are any familiar numbers in the given series.
- Familiar numbers are the numbers which 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 observe 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

## Practice Set On Number Series

**Directions(1-5):** Find the missing number in the following number series.

- 20 24 33 49 74 ?

A) 115

B) 88

C) 96

D) 110

E) 123 - 1 ? 27 64 125

A) 8

B) 11

C) 12

D) 16

E) None of these - 12 14 17 13 ? 14 21 13

A) 11

B) 8

C) 10

D) 12

E) None of these - 5 11 ? 55 117

A) 22

B) 25

C) 33

D) 30

E) None of these - 85 43 44 67.5 ? 345

A) 125

B) 140

C) 137

D) 112

E) None of these

**Directions(6-10):** In each of the following questions number series, there is a wrong number that does not follow the pattern of the series. Find the** wrong **number.

- 62 87 187 420 812 1437

A) 87

B) 187

C) 420

D) 812

E) None of these - 120 137 170 222 290 375

A) 137

B) 170

C) 222

D) 290

E) 375 - 550 542 537 521 496 460

A) 496

B) 521

C) 537

D) 542

E) 460 - 12 48 168 500 1260 2520

A) 500

B) 168

C) 48

D) 1260

E) 2520 - 24 536 487 703 670 742

A) 536

B) 487

C) 670

D) 703

E)742

**Directions(1-5**): In the following number series only one number is wrong. Find out the **wrong** number.

- 484 240 118 57 5 11.25 3.625

A) 26.5

B) 57

C) 5

D) 3.625

E) 240 - 5 7 16 57 244 1245 7506

A) 7506

B) 5

C)244

D) 7

E) 16 - 4 2.5 3.5 6.5 15.5 41.25 126.75

A) 41.25

B) 6.5

C) 126.75

D) 4

E) 2.5 - 210 209 211 186 202 77

A) 209

B) 77

C) 211

D) 186

E) 202 - 33 321 465 537 575 591 600

A) 465

B) 33

C) 600

D) 575

E) 591**Directions(6-10):**What should come in place of question mark in the following series. - 3 7 18 26 ? 53 64 96

A) 37

B) 30

C) 40

D) 35

E) 32 - 1.7 3.2 2.7 4.2 3.7 ? 4.7 6.2

A) 3.8

B) 5.2

C) 4.4

D) 4.8

E) 5.5 - 6 8 10 42 ? 770 4578

A) 110

B) 150

C) 132

D) 148

E) 115 - 7 13 31 85 247 ?

A) 733

B) 680

C)700

D) 650

E) 666 - 949 189.8 ? 22.776 11.388 6.8328

A) 39.98

B) 40.15

C) 48.53

D) 56.94

E) 55.55

**Directions(1-5):** What will come in place of question mark in the given number series.

- 17 9 15 40 5 ?

A) 620

B) 650.25

C) 550.5

D) 688

E) 540.15 - 2 9 25 82 335 ?

A) 1456

B) 1246

C) 1682

D) 1560

E) 1550 - 1548 516 129 43 ?

A) 9.82

B) 11.11

C)13.25

D)10.75

E) 11.25 - 41 164 2624 ? 6045696

A)94464

B) 84500

C)94502

D) 78542

E) 82456 - 4 9 29 119 599 ?

A) 2998

B) 4578

C) 3245

D) 2000

E) 3599**Directions(6-10):**In the following number series only one number is wrong. Find the**wrong**number. - 133 183 241 307 381 463 480

A) 307

B) 133

C) 480

D) 241

E) 381 - 31 15 21 50 155.3 767.25

A) 767.25

B) 155.3

C) 15

D) 31

E) 50 - 18 119 708 3530 14136 42405

A) 14136

B) 708

C) 119

D) 3530

E) 42405 - 500 484 451 384 260 80

A) 80

B) 260

C) 451

D) 484

E) 500 - 9 10.8 18 21.6 36 64.8

A) 21.6

B) 10.8

C) 36

D) 18

E) 9

**Directions (1-5): In the following number series, a wrong number is given. Find out that wrong number.**

**Q1. 2 11 38 197 1172 8227 65806**

**Q2. 16 19 21 30 46 71 107**

**Q3. 7 9 16 25 41 68 107 173**

**Q4. 4 2 3.5 7.5 26.25 118.125**

**Q5. 16 4 2 1.5 1.75 1.875**

**Directions (6-10) : In each of the following questions a number series is given. After the series a number is given followed by (a), (b), (c), (d) and (e). You have to complete the series starting with the given number, following the sequence of original series and answer the questions that follow the series.**

**Q6. 3 19 103 439 1381 2887**

**5 (a) (b) (c) (d) (e)**

**What will come in place of (b) ?**

**Q7. 4 13 40 135 552 2765**

**2 (a) (b) (c) (d) (e)**

**What will come in place of (c) ?**

**Q8. 5 12 4 10 3 8**

**6 (a) (b) (c) (d) (e)**

**What will come in place of (d) ?**

**Q9. 3 13 37 87 191 401**

**1 (a) (b) (c) (d) (e)**

**What will come in place of (d) ?**

**Q10. 8 4 6 15 52.5 236.25**

**12 (a) (b) (c) (d) (e)**

**What will come in place of (c) ?**

**Directions (11-15) : What should come in place of question mark (?) in the following number series ?**

**Q11. 13 14 30 93 376 1885 ?**

**Q12. 4 6 9 13.5 20.25 30.375 ?**

**Q13. 400 240 144 86.4 51.84 31.104 ?**

**Q14. 9 4.5 4.5 6.75 13.5 33.75 ?**

**Q15. 705 728 774 843 935 1050 ?**

**SOLUTION**:

**Directions (Q.1-5): What will come in place of the question mark (?) in the following number series?**

**Q1. 1401, 1402, 705, ?, 77**

**Q2. 10, 6, 12, 35, ?, 591.75**

**Q3. 390, 198, ?, 54, 30, 18**

**Q4. 10, 77, 474, ?, 9556, 28683**

**Q5. 150, 50, 131, 67, 116, ?, 105**

**Directions (Q.6-10): In each of these number series one number is wrong. Find out the wrong number.**

**Q6. 5, 6, 7.5, 9.75, 13.25, 18.4275**

**Q7. 13, 25, 41, 62, 85, 113**

**Q8. 250, 55, 16, 8.2, 6.1, 6.328**

**Q9. 18, 54, 162, 491, 1466**

**Directions (Q.11-15): In each of these questions, a number series is given. Below the series one number is given followed by (a), (b), (c), (d) and (e) You have to complete this series following the same logic as in the original series and answer the question that follows.**

**Q11. 5, 9, 25, 91, 414, 2282.5**

**3 (a) (b) (c) (d) (e)**

**What will come in place of (c) ?**

**Q12. 15, 9, 8, 12, 36, 170**

**19 (a) (b) (c) (d) (e)**

**What will come in place of (b) ?**

**Q13. 7, 6, 10, 27, 104, 515**

**9 (a) (b) (c) (d) (e)**

**What will come in place of (d) ?**

**Q14. 6, 16, 57, 244, 1245, 7506**

**4 (a) (b) (c) (d) (e)**

**What will come in place of (d) ?**

**Q15. 8, 9, 20, 63, 256, 1285**

**5 (a) (b) (c) (d) (e)**

**What will come in place of (e)**

**Solutions**

S6. Ans.(a)

Sol.

The pattern of the series is:

×1.2,×1.25,×1.3,×1.35,×1.4,×1.45……….

S7. Ans.(a)

Sol.

The pattern of series is:

+12,+16,+20,+24,+28

S8. Ans.(d)

Sol.

The series is:

÷5+5,÷5+5,÷5+5,÷5+5…….

S9. Ans.(d)

Sol.

The pattern of series is:

×3+1,×3-3,×3+5,×3-7,×3+9……

**4, 5, 6, 14, ?, 100.5**

1. 32.5

2. 47.5

3. 67.5

4. 37.5

5. 27.5**8 4 4 8 32 ?**

1.354

2.384

3.294

4.234

5.256**2, 2, 7, ?, 87, 342**

1.21

2.26

3.23

4.24

5.22**6, 8, 8, 22, ?, 151**

1.43

2.42

3.44

4.47

5.48**4, ?, 14, 40, 88, 170**

1.9

2.5

3.6

4.7

5.2**6, 6, 7, ?, 91, 463**

1.33

2.43

3.38

4.25

5.44**2, 5, 17, 50, 122, ?**

1.252

2.258

3.257

4.225

5.242**2, 9, 39, 161, ?, 2613**

1.675

2.670

3.665

4.651

5.655**5, ?, 20, 34, 76, 142**

1.4

2.5

3.7

4.8

5.9**5, 6, 8, 30, 136, ?**

1.645

2.680

3.650

4.690

5.620

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