**Reasoning | Magical Math**

**Type of number series:**

**Even series:-**

An even number is any number that can be divided by 2 exactly. The last digit of an even number is always one of the following: 0, 2, 4, 6, or 8. Even numbers can include 2, 4, 6, 8, 10, 12, and 14. These are even numbers because they are simple to divide by two. It is important to remember that 2 is the smallest positive even natural number. An odd number is one that you choose that cannot be split by two. Examples include 1, 3, 5, 7, 9, etc.

**Odd series:-**

An odd number is one that you choose that cannot be split by two. Examples include 1, 3, 5, 7, 9, etc.

**Prime series:-**

In everyday life and mathematics, numbers are everywhere. In mathematics, there are numerous different kinds of numbers. One of the significant ones is the prime number. A positive integer that can only be divided by itself and by the number one is a prime number. In other words, a prime number cannot be divided by any number other than 1 and itself.

**Square series:-**

A square number, perfect square, or simply “a square” is produced when you multiply an integer (a “whole” number, positive, negative, or zero) by itself. Therefore, square numbers include 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

**Cube series:-**

Numbers that are the triple product of the same number are known as perfect cubes. In other words, the value produced by multiplying a whole number by three times itself is a perfect cube. A number that may be expressed as three times the product of another integer is referred to as a perfect cube.

**Arithmetic series:-**

Sequences are lists of numbers in a certain order. A phrase is used to describe each number in the series. In most cases, the sequence exhibits patterns that let us anticipate what the subsequent phrase in the series will be. The sum of a series in which each component is computed from the preceding one by adding and subtracting constants is known as an arithmetic series. Alternately, we may say that an arithmetic progression is a set of numbers where, for every pair of consecutive terms, the second number is obtained by adding a fixed amount to the first.

The term “finite arithmetic progression” or “arithmetic progression” refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.

**In Arithmetic series there are two types**

- Two Tier series
- Three Tier series

In Two Tier series we will get answer in two steps

For example

4 8 12

In the first step we will find what is difference between 4 and 8 . There is difference of 4 .

Than difference between 8 and 12, It again 4.

In the second step the difference between first steps numbers.

Three Tier series

In Two Tier series we will get answer in three steps

For example

4 12 24 36

In the first step

We will find what is difference between 4 and 12 ,There is difference of 8 .

Difference between 12 and 24 ,There is difference of 12 .

Difference between 24 and 36 ,There is difference of 12 .

In the second step the difference between first steps numbers.

In the third step the difference between second steps numbers.

**Examples**

*Now let us see this with an example:-*

**1) 1 3 6 10 15 ?**

This number series is increasing order.

Now we will find out the difference between first two numbers that is 1 and 3 ,the differs is of 2 .

Than difference between 3and 6 , the differs is of 3

Difference between 6and 10 , the differs is of 4

Difference between 10and 15 , the differs is of 5

So to get the answer for ? ,we will study the differences that is 2 3 4 5 . It is in increasing order. For the answer the differs should have of 6 with it’s previous number in the series.

For that we will add 6 in number 15

15+6=21 , the answer is 21. As difference between 15 and 21 is 6.

**2) 87 80 74 69 65 ?**

We have to identify the order of number series . Here we see this is decreasing order number series.

Now we will find out the difference between first two numbers that is 87 and 80 ,the differs is of 7 .

Than difference between 80and 74 , the differs is of 6

Difference between 74 and 69 , the differs is of 5

Difference between 69 and 65 , the differs is of 4

So next difference in number will be 3.

We have to find out 3 number smaller figure than 65

65-3=62, 62 is the answer

**3) 40 15 30 25 20 35 ?**

In this series of number we see one number up other down

We will find out difference between numbers

Difference between 40 and 15 is 25 .

Difference between 15 and 30 , is 15

Difference between 30 and 25 , is 5

Difference between 25 and 20 , is 5

To get the answer for ? ,we will study the differences that is 25 15 5 5 15 So next difference between numbers will be of 25

**4) 1 4 9 25 ?**

This number series is neither increasing nor decreasing order.

This is square number series

Square of 1 is 1 , Square of 2 is 4, Square of 3 is 9, Square of 5 is 25

So answer will be Square of 6 is 36

**4) 1 8 27 64 125 ? ? ? 729 1000**

This number series is neither increasing nor decreasing order.

This is cube number series

cube of 1 is 1 , cube of 2 is 8, cube of 3 is 27, cube of 4 is 64, cube of 2 is 125

So next cube of 6 is 216, cube of 7 is 343, cube of 8 is 512 are the answers.

**5) 10 18 15 23 20 28 ?**

This is some different numbers series

we will find out the difference between the numbers

Difference between 10 and 18 is 8

Difference between 18 and 15 is 3

Difference between 15 and 23 is 8

Difference between 23 and 20 is 3

Difference between 20 and 28 is 8

Here we are getting 8,3 8, 3 sequence

Next difference will be 3

So 28-3 = 25 is the answer

**6) 19 24 20 25 21 26 ?**

This is some different numbers series

we will find out the difference between the numbers

Difference between 19 and 24 is 5

Difference between 24 and 20 is 4

Difference between 20 and 25 is 5

Difference between 25 and 21 is 4

Difference between 21 and 26 is 5

Here we are getting 5,4 ,5,4 sequence

Next difference will be 4

So 26-4=22 is the answer