Consecutive numbers are the numbers that continuously follow each other, one after another in a regular counting order or in the order from smallest to largest.
Consider the natural numbers. The numbers 1, 2, 3, 4,… are consecutive numbers.
The formula for consecutive numbers (assuming that the numbers follow each other by the difference of 1) can be written as x, x+1, x+2, x+3, …, and so on.
Properties of Consecutive numbers:
- The difference between any predecessor-successor pair for consecutive numbers is always fixed. It can be 1 or more than 1.
- For any two consecutive even numbers, the difference is always 2.
For example, 8 and 10 are two consecutive odd numbers, their difference = 10 - 8 = 2.
- For any two consecutive odd numbers, the difference is also 2.
For example, 16 and 18 are two consecutive even numbers, their difference = 18 - 16 = 2.
- If “n” is an odd number, then the sum of “n” consecutive numbers will be divisible by “n.” For example, the sum of these 3 consecutive numbers is 2 + 3 + 4 = 9 which is divisible by 3.
- The product of any three consecutive integers, is always divisible by 6.
2 × 3 × 4 = 24
8 × 9 × 10 = 720
Find the Consecutive numbers when the sum is given:
Let us suppose the sum of two consecutive numbers is 75.
So, we know that two consecutive numbers are of the form n, n+1
Sum =75
n + n + 1 = 75
2n = 74
⇒n = 37
n + 1 = 37 + 1 = 38
So, the consecutive numbers whose sum is 75 is 37 and 38.
Find the Consecutive numbers when the product is given:
Let us suppose the product of two consecutive numbers is 30.
We will find the two perfect squares between which the product lies. Keep in mind that the perfect squares should belong to consecutive numbers.
We know that 5 × 5 = 25 and 6 × 6 = 36.
So, the consecutive numbers whose product is 30 are 5 and 6.
