##### Maths TricksStudy Notes

# Maths Tips Number Series, Formulas, Problems

**Difficulty level – Easy : **(By keen observation itself, you can easily find pattern.)

*Prime numbers*

2, 3, 5, 7, 11

**Squares of numbers **

1, 4, 9, 16, 25

169, 225, 289, 361, 441 – squares of odd number

(13^{2}, 15^{2}, 17^{2}, 19^{2}, 21^{2})

*Addition/subtraction by a common number*

Example : 11, 14, 17, ? , 23

** Difference between successive numbers **are

*3.*so 17 + 3 = 20 is answer

Example : 975, 962, ?, 936 , 923 .

Difference between successive numbers are 13 and they are in decreasing order so answer will be 962 – 13 = 949.

** Multiplication/ division**

In this pattern, a certain number is multiplied or divided with the previous number to get next number in the series.

**Example** : 15, 30, 60, 120, 240

15*2 = 30

30 *2= 60

60*2 = 120

120*2 = 240

**Example** : 5172, 2536, 1268, 634, 317

5172÷2=2536

2536÷2=1268

1268÷2=634

634÷2=317

If you are not able to find the pattern by observing the question, you have to follow the below procedures

** Difficulty level – moderate** : ( from here real problems start, no need to panic for that, patiently understand the procedure and try to solve, it will be easy while you are scrolling down )

- In such type of questions, we have to find the difference between consecutive numbers
- Difference between consecutive numbers will follow a pattern (consecutive addition/subtraction or multiplication/division).

**Example 1**: 30, 46, 78, 126, 190, 270, ?

Difference between 30 & 46 is 16

Difference between 46 & 78 is 32

Difference between 78 & 126 is 48

Difference between 126 & 190 is 64

Difference between 190 & 270 is 80

Here the differences are all multiples of 16 i.e. (16*1), (16*2), (16*3), (16*4), (16*5), so obviously the next number will be (16*6).

So in series the next number will be addition of (16*6 =) 96 therefore the answer is 270+96 = 366

**Example 2**: 17, 20, 26, 38, 62, 110

Find the difference between the numbers, and the differences are

Difference between 17 & 20 = 3

Difference between 20 & 26 = 6 (3*2)

Difference between 26 & 38 = 12 (6*2)

Difference between 38 & 62 = 24 (12*2)

Difference between 62 & 110 = 48 (24*2)

**Example 3**: 1250, 500, 200, 80, 32, 12.8, ?

Whenever you see a decimal number in series, your guess for the number should be a decimal digit or division process Here too a decimal number is multiplied or divided to form this series.

1250÷2.5 = 500

500÷2.5=200

200÷2.5= 80

80÷2.5=32

32÷2.5=12.8

12.8÷2.5=5.12

**Example 4**: 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: **If the difference between consecutive numbers do not follow any patterns, try these patterns

(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.

TIPS:To find the pattern try this technique.

Multiply the number before last number with 2 and compare the resultant number with the last number

- 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).

**Solving these problems will make you understand better.**

**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

difference between 3&732 = 729 i.e. 9^{3}

difference between 732&1244 = 512 i.e.8^{3}

difference between 1244&1587 = 343 i.e. 7^{3}

difference between 1587&1803 = 216 i.e. 6^{3}

difference between 1803&1928 = 125 i.e. 5^{3}

obviously next will be addition of 4^{3}+ 1928 = 1992

**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 1885

So pattern is 376*5+5=1885

13*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