# Notes: All About Number Series

__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 .

__Different types of Number Series__

There are some format of series which are given in Exams.

__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: **441, 484, 529, 576?

__Answer:____ __441 = 21^{2}, 484 = 22^{2}, 529 = 23^{2}, 576 = 24^{2 }, 625 = 25^{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 2:** 1331, 1728, 2197, ?

** Answer :** 11

^{3}, 12

^{3}, 13

^{3}, 14

^{3}

__Geometric Series:__

This type of series are based on ascending or descending order of numbers and each successive number is obtain by multiplying or dividing the previous number with a fixed number.

**Example 3: **5, 45, 405, 3645,?

__Answer:__** **5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 = 32805.

__Two stage Type Series:__

A two tier Arithmetic series is one in which the differences of successive numbers themselves form an arithmetic series.

**Example 4:** i. 3, 9, 18, 35, 58,——

- 6, 9, 17, 23,———-

__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.

__Examples 5: __

11, 24, 50, 102, 206, ?

__Answer:__** **

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.

**Number Series Quiz**

**Directions (1-10****): What will come in place of the question marks (?) in the following Number series?**

- 0, 6, 24, 60, 120, 210, ?
- 336
- 349
- 312
- 337
- None of these

- 11, 14, 19, 22, 27, 30, ?
- 39
- 34
- 36
- 35
- None of these

- 6, 12, 21, ? , 48
- 33
- 39
- 36
- 31
- None of these

- 18, 22, 30, ? ,78, 142
- 44
- 35
- 46
- 48
- None of these

- 73205, 6655, 605, 55, ?
- 9
- 5
- 13
- 11
- None of these

- 25, 100, ?, 1600, 6400
- 400
- 300
- 360
- 420
- None of these

- 125, ?, 343, 512, 729, 1000
- 216
- 215
- 256
- 225
- None of these

- 1 , 9 , 125 , 343 , ? , 1331
- 730
- 729
- 512
- 772
- None of these

- 121, 144, 169, ?, 225
- 180
- 172
- 186
- 196
- None of these

- ?, 2116, 2209, 2304, 2401, 2500
- 2124
- 1972
- 1521
- 2025
- None of these

**Answers with Explanation:-**

- (A)
The given series is : 1

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

So the missing term = 7^{3}– 7 = 343 – 7 = 336 .

- (D)

The pattern is + 3, + 5, + 3, + 5, …………

So the missing term is = 30 + 5 = 35 .

- (A)

The pattern is + 6, + 9, + 12, +15 ………..

So the missing term is = 21 + 12 = 33 .

- (C)

The pattern is +4, +8, +16, +32, +64

So the missing term is = 30 + 16 = 46 .

- (B)

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

- (A)

25 x 4 = 100, 100 x 4 = 400, 400 x 4 = 1600, 1600 x 4 = 6400.

**(A)**

125 = 5^{3} , 216 = 6^{3}, 343 = 7^{3}, 512 = 8^{3}, 729 = 9^{3}, 1000 = 10^{3}.

**(B)**

1^{3} , 3^{3} , 5^{3} , 7^{3} , 9^{3} , 11^{3}

- (D)

121 = 11^{2}, 144 = 12^{2}, 169 = 13^{2}, 196 = 14^{2}, 225 = 15^{2}.

- (D)

__ __2025 = 45^{2}, 2116 = 46^{2}, 2304 = 48^{2}, 2401 = 49^{2}, 2500 = 50^{2}

__TIME TAKEN__

Within 5 min : EXCELLENT

5-8 min : YOU CAN DO BETTER

More than 8 min : YOU NEED TO WORK HARD

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