The number system is made up of odd and even numbers. An odd number pattern is a sequence or series of odd numbers. The purpose of the odd number pattern is to help the students to recognize the difference between odd numbers and even numbers. This odd pattern establishes the relation between the odd numbers. Know how to find the odd number patterns from here.

The formula to find the odd number pattern is 2n + 1, 2n + 3, 2n + 5, 2n + 7….

Do Refer:

## What is an Odd Number Pattern?

A sequence of odd numbers to prove their sum is known as odd number patterns. Generally, the odd numbers are 1, 3, 5, 7, 9.. and so on. We can find the sum of odd numbers easily by using arithmetic progression.

- The sum of odd numbers is even numbers.
- The product of two odd numbers is odd numbers.
- The sum of one odd number and one even number is an odd number.

### What is the sum of n Consecutive Odd Numbers?

The odd number sequence is to prove their sum. The sum of the first odd number is 1 is always equal to the square of the number of digits added together.

The sum of first n odd numbers are 1, 3, 5…. (2n – 1)

The sum of odd numbers is n²

**Example:**

What is the sum of the first two odd numbers?

**Solution:**

Odd numbers = 1, 3, 5

So, the sum of first two odd numbers = 1 + 3 = 4

Thus the sum of the first two odd numbers is 4.

### Examples on Odd Number Patterns

**Example 1.**

What is the sum of the first four odd numbers?

**Solution:**

The sum of odd numbers = 1, 3, 5…. (2n – 1)

a + b + c + d = n

n = 1 + 3 + 5 + 7

n = 16

Thus the sum of first four odd numbers is 16.

**Example 2.**

What is the sum of odd numbers from 1 to 20?

**Solution:**

The sum of odd numbers = 1, 3, 5…. (2n – 1)

Odd numbers from 1 to 20 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Sn = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

Sn = 100

There are 10 odd numbers from 1 to 20.

Sn = n²

Sn = 10² = 100.

**Example 3.**

What is the product of the first three odd numbers?

**Solution:**

The first three odd numbers are 1, 3, 5

The product of the first three odd numbers are 1 × 3 × 5 = 15

Therefore the product of the first three odd numbers is 15.

**Example 4.**

What is the sum of one even number and one odd number?

**Solution:**

Let the even number be 8

Let the odd number be 9

8 + 9 = 17

17 is an odd number.

Thus the sum of one even number and one odd number is an odd number.

Hence it is proved that the sum of an even number and an odd number is an odd number.

**Example 5.**

What is the product of one even number and one odd number?

**Solution:**

Let the even number be 6

Let the odd number be 7

6 × 7 = 42

42 is an even number.

Thus the product of one even number and one odd number is an even number

Hence it is proved that the product of an even number and an odd number is an even number.

### FAQs on Odd Number Pattern

**1. What is an odd number sequence?**

An odd number sequence is a pattern of odd numbers. The total of any set of sequential odd numbers beginning with 1 is always equal to the square of the number of digits, added together

**2. What are the rules for odd and even numbers?**

1. An odd number can only be formed by the sum of an odd and even number.

2. An odd number can only be formed by multiplication in one way: odd·odd = odd.

3. An even number can only be formed by multiplication in three ways: even·odd, odd·even, and even·even.

**3. Why is the sum of an odd and even number odd?**

When adding two of the addends together at a time, the answer rotates between even and odd. When the final two numbers are added together, one is even and the other odd. Therefore, the sum is odd, which makes the product odd since it is equivalent to the sum.