Number Sense - Consecutive Numbers

• Consecutive Numbers
• Successor 
• Predecessor
• Even Consecutive Numbers
• Odd Consecutive Numbers
• Solved Examples
• Practice Problems
• Frequently Asked Questions

Consecutive Numbers

Consecutive numbers are the numbers that follow a sequence where each number comes after the previous number without any gap. These numbers adhere to a pattern where the difference between any two consecutive numbers remains constant, without skipping the number in between. For instance `1, 2, 3, 4, 5, 6, 7,` ……..and so on. We can also have consecutive negative numbers. For instance `-10, -9, -8, -7, -6,`..... and so on.

In other words, each number is one more than the previous number.

Formula: For any integer `x`, consecutive numbers can be found using the pattern given below:

`x, x + 1, x + 2, x + 3, x + 4,`........... and so on.

Predecessor

A number that comes immediately before the given number is called the predecessor of the given number. For instance, let’s find the predecessor of the following consecutive numbers such as  `9, 10, 11`

`8` is the predecessor of `9` since it appears before `9` in the sequence of numerals.

Similarly, `9` is the predecessor of `10`, and `10` is the predecessor of `11`.

Successor

A number that follows immediately after the given number is called the successor of the given number. For instance, `10` is the successor of `9`, since it appears after `9` in the sequence.

Even Consecutive Numbers

The numbers that are exactly divisible by `2` are called even integers. For instance, `0, 2, 4, 6, 8, 10, 12, `……..and so on.

Note: The difference between the predecessor and successor of even consecutive numbers is `2`.

“Even integers that follow the consecutive number rule are called even consecutive numbers.”

Example: List the even consecutive numbers between `13` and `23`.

Answer: Even consecutive numbers between `13` and `23` are `14, 16, 18, 20, 22`.

We can observe the following points from the above answer:

• Even consecutive integers are divisible by `2`.
• The difference between two consecutive even integers is `2`.
• The predecessor of `16` is `14`, of `18` is `16`, of `20` is `18`, and of `22` is `20`.
• The successor of `14` is `16`, of `16` is `18`, of `18` is `20`, and of `20` is `22`.

Formula: If `x` is an integer then we can find the even consecutive numbers by the following pattern given below:

`2x, 2x + 2, 2x + 4, 2x + 6, 2x + 8,` ……….and so on.

Odd Consecutive Numbers

The numbers that are not divisible by `2` are called odd integers. For instance, `1, 3, 5, 7, 9, 11, 13, 15,`.......and so on.

Note: The difference between the predecessor and successor will be `2` for odd consecutive numbers.

Example: List the odd consecutive numbers between `21` and `30`.

Solution: `21, 23, 25, 27, 29`

We can observe the following points from the answer:

• Odd consecutive integers are not divisible by `2`.
• The difference between two odd consecutive integers is `2`.
• The predecessor of `23` is `21`, of `25` is `23`, of `27` is `25`, and of `29` is `27`.
• The successor of `21` is `23`, of `23` is `25`, of `25` is `27`, and of `27` is `29`.

Formula: If `x` is an integer then we can find the odd consecutive numbers by the following pattern given below:

`2x + 1, 2x + 3, 2x + 5, 2x + 7, 2x + 9,` ……….and so on.

Solved Examples

Q`1`. What are the missing numbers from the given consecutive numbers pattern?

`23, 24, ……, ……, 27, 28`.

Solution: 

Since the given numbers are consecutive. The processor of `27` is `26` and the successor is `24` is `25`.

Therefore, the missing numbers are `25` and `26`.

Q`2`. If the sum of two consecutive numbers is `57`, what are the numbers?

Solution: 

Let the two consecutive numbers be `x` and `x + 1`.

We know:  `x + (x + 1) = 57`

`2x + 1 = 57` 

`2x = 57 - 1`

`2x = 56`

`x = 28`

Thus the consecutive numbers are `28` and `29`.

Q`3`. If the sum of the three even consecutive numbers is `78`, what are these even consecutive numbers?

Solution: 

Let `2x, 2x + 2, 2x + 4` be the three even consecutive numbers.

The sum of three even consecutive numbers = `78`

`2x + (2x + 2) + (2x + 4) = 78`

`6x + 6 = 78`

`6x = 72`

`x = 12`

`2x = 24`

`2x + 2 = 2 × 12 + 2 = 26`

`2x + 4 = 2 × 12 + 4 = 28`

Therefore, three even consecutive numbers are `24, 26, 28`. 

Q`4`. If the sum of the two odd consecutive numbers is `44`, what are these odd consecutive numbers?

Solution: 

Let the two odd consecutive numbers be  `2x + 1` and `2x +3`.

The sum of two consecutive odd numbers = `43`

`(2x + 1) + (2x + 3) = 44`

`4x + 4 = 44`

`4x = 44 - 4`

`4x = 40`

`x = 10`

`2x + 1 = 2 × 10 + 1 = 21`

`2x + 3 = 2 × 10 + 3 = 23`

Therefore, two consecutive odd numbers are `21 and 23`.

Q`5`. Write three positive consecutive numbers and three negative consecutive numbers.

Solution: 

Positive consecutive numbers `= 1, 2, 3`

Negative consecutive numbers `= −3, −2, −1`

Practice Problems

Q`1`. The missing numbers of the given pattern are…..

`22, ……, 26, …….., 30, 32, 34`

1. `23, 25`
2. `24, 28`
3. `25, 26`
4. `28, 29`

Answer: b

Q`2`. The difference between two odd consecutive numbers is…..

1. `3`
2. `4`
3. `2`
4. `1`

Answer: c

Q`3`. The formula for an odd consecutive number starts with ……….

1. `2x`
2. `x + 1`
3. `2x + 1`
4. `3x`

Answer: c

Q`4`. The formula for an even consecutive number starts with ……..

1. `2x`
2. `2x + 1`
3. `3x`
4. `x`

Answer: a

Q`5`. The predecessor of `50` is ……….

1. `51`
2. `52`
3. `49`
4. `55`

Answer: c

Frequently Asked Questions

Q`1`. What are consecutive numbers?

Answer: Consecutive numbers are integers that follow each other in sequence with a constant difference of `1`. For example, `2, 3, 4, 5` are consecutive numbers.

Q`2`. Can odd consecutive integers have a common difference other than `2`?

Answer: No, the common difference between odd consecutive integers is always `2`. This is because odd integers are spaced alternately on the number line, and the difference between any two consecutive odd integers is `2`.

Q`3`. What is the predecessor of a given number?

Answer: The predecessor of a number is the integer that comes immediately before it. For any integer \( n \), its predecessor is \( n - 1 \).

Q`4`. How can I find the successor of an even number?

Answer: The successor of an even number is the next integer that comes immediately after it. If \( n \) is an even number, then its successor is \( n + 1 \).