Sum of Consecutive Numbers Shortcut

sum of consecutive numbers shortcut

Finding the sum of consecutive numbers is a common question asked in competitive exams. You can now find the sum of consecutive numbers starting with 1, sum of consecutive odd numbers and sum of consecutive
even numbers in seconds.

What are consecutive numbers?

Numbers that follow each other in order are Consecutive numbers.Here the difference between every two numbers is 1. The consecutive numbers can be represented as n,n+1,n+2.
Examples of consecutive numbers:
(1)1,2,3,4,5,6,7,8
(2)6,7,8,9,10,11

Sum of consecutive numbers starting from 1 shortcut

Now that we know what consecutive numbers are.We shall see a shortcut to find sum of consecutive numbers starting from 1.
It can be represented as Sum of n consecutive numbers = n+(n+1)+(n+2)

Sum of consecutive numbers starting from 1 shortcut steps

Step 1:Count the total number of integers from 1 to the last consecutive number given.
Step 2:Multiply the result in step 1 by 1 more than the number.
Step 3:Divide the result of step 2 by 2.

We shall see some examples to understand better
Example 1:Find the sum of all consecutive numbers from 1 to 9.
Step 1: Counting number of integers from 1 to 9. We find that there are 9 integers.

Step2: Multiplyig the number of integers(9) by 1 more than the number that is 10.
We get, 9 X 10=90

Step3: Dividing the result obtained in step2 by 2
we get, 90/2=45

Ans Hence, sum of consecutive numbers from 1 to 9=45

Example 2:Find the sum of all consecutive numbers from 1 to 99.
Step 1: Counting number of integers from 1 to 99. We find that there are 99 integers.

Step2: Multiplyig the number of integers(99) by 1 more than the number that is 100.
We get, 99 X 100=9900

Step3: Dividing the result obtained in step2 by 2
we get, 9900/2=4950

Ans Hence, sum of consecutive numbers from 1 to 99=4,950

Odd Consecutive numbers

Odd numbers that follow each other are consecutive odd numbers. Here the difference between every two odd numbers is 2.
It can be represented as Sum of n numbers = n+(n+2)+(n+4)+(n+6) where n is an odd number..
We shall see how to add odd consecutive numbers.

Sum of consecutive odd numbers starting from 1 steps

Step 1: Count the total number of odd integers from 1 to the last consecutive number given.
Step 2: Square the result obtained in step 1.

Example 1:Find the sum of all consecutive odd numbers from 1 to 10.
Step 1: Counting number of integers from 1 to 9. We find that there are 5 integers.
Step 2: Squaring the result obtained in step 1.
We get, 52=25
Ans hence, Sum of odd numbers from 1 to 9 is 25

Example 2:Find the sum of all consecutive odd numbers from 1 to 100.
Step 1: Counting number of integers from 1 to 100. We find that there are 50 integers.
Step 2: Squaring the result obtained in step 1.
We get, 502=2500
Ans 2500

Even Consecutive numbers

Even numbers that follow each other are consecutive even numbers. Here the difference between every two even numbers is 2.
It can be represented as Sum of n numbers = n+(n+2)+(n+4)+(n+6)where n is an even number.
We shall see how to add even consecutive numbers.

Sum of consecutive even numbers starting from 2 steps

Step 1: Count the total number of odd integers from 1 to the last consecutive number given.
Step 2: Multiply the result in step 1 by 1 more than the number.

Example 1:Find the sum of all consecutive even numbers from 1 to 10.

Step 1: Counting number of integers from 1 to 10. We find that there are 5 integers.
Step 2: Multiplying the number of integers(5) by 1 more than the number that is 6.
We get, 5 X 6=30
Ans 30

Example 2:Find the sum of all consecutive even numbers from 1 to 100.
Step 1: Counting number of integers from 1 to 100. We find that there are 50 integers.
Step 2: Multiplying the number of integers(50) by 1 more than the number that is 51.
We get, 50 X 51=2550
Ans 2550.

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