Product of two consecutive odd or even natural numbers

Table of Contents

• Product of 2 Consecutive Odd or Even Natural Numbers
• What’s Next?

In the previous segment, we learnt about the relationship between consecutive numbers and square numbers. In this segment, we will look at the product of two consecutive odd or even natural numbers.

What is the relationship between square numbers and the product of 2 consecutive odd or 2 consecutive even numbers?

If (a-1) and (a+1) are 2 consecutive odd or even numbers, then, (? − 1) × (? + 1) = ?² − 1

Let us understand this with a few examples.

• Consider the consecutive odd numbers 11 and 13. Here, a – 1 = 11 and a + 1 = 13. Therefore, a = 12.

So as per the above mentioned property, 11 x 13 = 12² − 1

Let us verify this.

11 x 13 = 143

12² − 1 = 144 − 1 = 143

• Consider the consecutive even numbers 8 and 10. Here, a – 1 = 8 and a + 1 = 10. Therefore, a = 9

So as per the above mentioned property, 8 x 10 = 9² − 1

Let us verify this.

8 x 10 = 80

9² − 1 = 81 − 1 = 80.

What’s next?

In the next segment of Class 8 Maths, we will look at a few more patterns in square numbers.