The sum of two consecutive numbers is 21 What are the numbers

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

For example:

1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Consecutive Even Numbers:

Even numbers are numbers that end with 0, 2, 4, 6 or 8. The examples of consecutive even numbers are:0, 2, 4, 6, 8, 10, 12, …. 

Consecutive Odd Numbers:

Odd numbers are numbers that end with 1, 3, 5, 7 or 9. The examples of consecutive odd numbers are:1, 3, 5, 7, 9, 11, 13, 15, …. 

Consecutive Even and Odd Integers:

We can also have consecutive even and odd integers.

Example: Consecutive Even Integers:  – 8, –6, –4, –2, 0, 2, 4, 6, …..

Example: Consecutive Odd Integers: –9, –7, –5, –3, –1, 1, 3, 5, 7, ….The term consecutive numbers is often used to frame word problems.

Example: The sum of two consecutive numbers is 55. What are the numbers?

Here, let the first number be a. Since the numbers are consecutive, the other number will be a + 1

We now form an equation as per the given information:

Sum of the numbers = 55 =  a + a + 1

We should choose the numbers such that their sum is 55.

26 is nearly half of 55.

Let the two number be 26 and 27;

26 + 27 = 53   ✘

So, the two numbers are not 26 and 27.

Let us choose the next number, 28. So, the two numbers are 27 and 28.

27 + 28 = 55 ✓Therefore, the numbers are 27 and 28. 

Example: The product of two consecutive odd numbers is 143. What are the numbers?

We should choose the numbers whose product is nearly 143.

We know that 12 × 12 = 144

But, 12 is an even number.

Consecutive odd numbers near 12 are 11 and 13.

Let us find their product; 11 × 13 = 143 ✓Therefore, the numbers are 11 and 13.