Adding odd numbers

Table of Contents

• Relationship between Square Numbers and Odd Numbers
  • Adding Odd Numbers
  • Subtracting Odd Numbers
• Summary
• What’s Next?

In the previous segment, we learnt about numbers between square numbers. In this segment, we will find out if there is any relationship between square numbers and odd numbers.

What is the relationship between square numbers and odd numbers?

We will understand if there is any pattern related to square numbers when odd numbers are added or subtracted.

Addition of odd numbers

The sum of the first ‘n’ odd numbers is ?². This means adding successive odd numbers starting from 1, gives a square number.

Let us understand this.

Consider the first five odd numbers 1, 3, 5, 7, 9

If n = 2, that is we consider the first 2 odd numbers, 1 and 3, then their sum should be equal to 2²

1 + 3 = 4 and 2² = 4

Let us see if this true when we consider the first 3 and first 4 odd numbers.

• Sum of first 3 odd numbers = 1 + 3 + 5 = 9 = 3²
• Sum of first 4 odd numbers = 1 + 3 + 5 + 9 = 16 = 4²

Subtraction of odd numbers

If successive odd numbers are subtracted from a number to give zero, then the given number is a perfect square.

Let us understand this with an example.