Number Series is the arrangement of numbers in a certain order where some numbers are wrongly keptÂ or some numbers are missing from that series. So accurate series are found. They are divided into two. One is **missing series** and the other is **wrong series**.

1. **Easy**–Â Under easyÂ type, there are two scenarios.

__Scenario 1__: One is based on addition/subtraction by common difference

__Scenario 2__: Other is based on multiplication/division-Here a certain no. is multiplied or divided to the previous number to get the next number.

2. **ModerateÂ **– a) we need to find out common difference and b)pattern of common difference (addition, subtraction, multiplication, division).

3. **DifficultÂ **– Here common difference does not follow the pattern.

**Wrong number series **– In this series all the numbers will be followed by one rule except the one which is wrong.

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

**Solution**:

- \(29^{2}\), \(39^{2}\), \(49^{2}\), \(59^{2}\), \(69^{2}\)

**Example 2**:

1, 9, 25, ?, 81, 121

**Solution**:

- \(1^{2}\), \(3^{2}\), \(5^{2}\), \(7^{2}\), \(9^{2}\), \(11^{2}\)

**Example 3**:

289, 225, 169, ?, 81

**Solution**:

- \(17^{2}\), \(15^{2}\), \(13^{2}\), \(11^{2}\), \(9^{2}\)

**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

**Solution**:

- \(15^{3}\), \(22^{3}\), \(29^{3}\), \(36^{3}\), \(43^{3}\)

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

**Example 2**:

729, 6859, 24389, ?, 117649, 205379

**Solution**:

- \(9^{3}\), \(19^{3}\), \(29^{3}\), \(39^{3}\), \(49^{3}\), \(59^{3}\)

**Example 3**:

1000, 8000, 27000, 64000, ?

**Solution**:

- \(10^{3}\), \(20^{3}\), \(30^{3}\), \(40^{3}\), \(50^{3}\)

**Ration Series**:

This type of series are based on ration series, where sequence are in form of ratio in difference between the numbers. All numbers are arranged in ratio sequence order.

**Example 1**:

11, 22, 44, 88, ?

**Solution**:

- Separate each number and

= 11 x 2 = 22,

= 22 x 2 = 44,

= 44 x 2 = 88,

= 88 x 2 = 176.

**Example 2**:

13, 26, 412, ?, 1648

**Solution**:

- Separate each number and

= (1+1 = 2, 3+3 = 6) = 26,

= (2+2=4, 6+6 = 12) = 412,

= (41+41=82, 2+2=4 = 824,

= (82+82=164,4+4= 8)=1648.

So, the missing term is 824.

**Geometric Series**:

This type of series are based on ascending or descending sequence of numbers and each continuous number is obtain by multiplying or dividing the preceding number with static number.

**Example 1**:

3, ?, 45, 144, 585

**Solution**:

- 3 x 0 +9 = 9, 9 x 1 + 9 = 18, 18 x 2 + 9 = 45, 45 x 3 + 9 = 144, 144 x 4 + 9 = 585.

**Example 2**:

5, 45, 405, 3645, ?

**Solution**:

- 5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 = 32805.

**Example 3**:

73205, 6655, 605, 55, ?

**Solution**:

- 5 x 11 = 55, 55 x 11 = 605, 605 x 11 = 6655, 6655 x 11 = 73205.

**Two stage Type Series**:

A two stage Arithmetic series is one in which the formation of arithmetic series are obtain from differences of continuous numbers themselves.

**Example**:

1, 3, 6, 10, 15…..

**Solution**:

- 3 – 1 = 2, 6 – 3 = 3, 10 – 6 = 4, 15 – 10 = 5….

Now, we get an arithmetic sequence 2, 3, 4, 5

**Mixed Series**:

This type of series are more than one different order are given in a series which arranged in alternatively in a single series or created according to any non-conventional rule. This mixed series Examples are describes in separately.

**Example**:

11, 24, 50, 102, 206, ?

**Solution**:

- 11 x 2 = 22 +2 = 24,

24 x 2 = 48 + 2 = 50,

50 x 2 = 100 + 2 = 102,

102 x 2 = 204 + 2 = 206,

206 x 2 = 412 + 2 = 414.

So the missing number is 414.

- GivenÂ series 291, 304, 317, ?, 343

First, find the common difference between the numbers

i.e. 304 – 291 = 13

317 – 304 = 13

Now, just add 13 to 317

â‡’ 317 + 13 = 330

Therefore series is 291, 304, 317,

**2. Find out the series 9, 18, 36, 72, ?**

**Solution**:

- Given series is 9, 18, 36, 72, ?

Notice that every number is a multiple of 2 i.e.

9 Ã— 2 = 18

18 Ã— 2 = 36

36 Ã— 2 = 72

72 Ã— 2 = 144

Therefore, the series is 9, 18, 36, 72,

**3. Find out the series 30, 45, 75, 120, 180, 255, ?**

**Solution**:

- Given series 30, 45, 75, 120, 180, 255, ?

First, find out the common difference between the numbers i.e.

45 – 30 = 15

75 – 45 = 30

120 – 75 = 45

180 – 120 = 60

Now see the pattern of common difference i.e.

15 Ã— 1 = 15

15 Ã— 2 = 30

15 Ã— 3 = 45

15 Ã— 4 = 60

15 Ã— 5 = 75

15 Ã— 6 +

Therefore, the series is 30, 45, 75, 120, 180, 255,

**4. Find out the series 9, 90, 154, 203, 239, 264, ?**

**Solution**:

- Given series 9, 90, 154, 203,

Multiply second last number by 2 i.e. 2 Ã— 239=478 > 264

So, take common difference between them

90 – 9 = 81

154 – 90 = 64

203 – 154 = 49

239 – 203 = 36

264 – 239 = 25

By observing theÂ above pattern, they are square numbers i.e \(9^2, 8^2, 7^2, 6^2, 5^2, 4^2\) respectively

So, \(4^2\) + 264 = 280

Therefore, series is 9, 90, 154, 203, 239, 264,

**5. Find out the series 7, 13, 25, 49, 97, 194, 385?**

**Solution**:

- Given series 7, 13, 25, 49, 97, 194, 385?

7 Ã— 2 – 1 = 13

So, 13 Ã— 2 – 1 = 25

25 Ã— 2 – 1 = 49

49 Ã— 2 – 1 = 97

97 Ã— 2 – 1 = 193

193 Ã— 2 – 1 = 385

Therefore, the wrong number is 194