# Short cuts for addition

Addition is a basic concept and we all know how to add two numbers but question arises how much time we are consuming and do really question deserves worth of time.

Many times, we come across questions in which we have to add just numbers. Questions are easy but we consume so much time in addition. Here, we come with some short tricks for addition of consecutive numbers, odd numbers, square numbers etc. so that you consume less time in a question and save time for other questions.

You’ll come to know about each trick one by one.

## Addition of Consecutive Numbers

By Consecutive numbers, we mean to say numbers which are in particular order; whose common difference is same.

Example:

- 1,2,3,4,5,6,7…

Difference between all numbers is same. So, these are consecutive numbers.

- 5,8,11,14,17….

Again difference between numbers is same, So, these are consecutive numbers.

*Now, let us solve any question by short-cut method. *

Question 1. Find Sum of 5,12,19,26,33 .

Ordinary method:

Add all numbers and you will get answer 95.

Shortcut method;

Add first number and last number i.e; 5+33= 38

Multiply that sum by total numbers in the sequence. i.e; 38*5= 190

Divide the result by 2 i.e; (190/2)= 95

That’s it; you got answer by applying shortcut trick in just 2-5 sec.

### Addition of numbers whose range starts from 1

Suppose, Examiner asked you to find out the sum of the all odd numbers range starts from 1 to 100. No need to get panic, we had solution for this problem also.

*Square the amount of total numbers in the series.*

As you can see, there would be 50 odd numbers in the series of 1 to 100. So, sum of all odd numbers would be 50*50= 2500.

### Sum of all even number starting from 2

Suppose, series is same; 1 to 100.

There are two methods to solve this question. Find sum of all numbers of the series 1 to 100 and then subtract sum of odd numbers.

Otherwise, we also have an alternate solution for this question also.

Multiply the Amount of numbers by one more than the number.

As you can see, there would be 50 even numbers in the list. So, answer is 50*51= 2550.

### Adding a series of numbers having common ratio

This is little bit tricky question. Because, you can’t apply addition method as common difference is not same.

Question: Find sum of 95,190,380,760.

**Answer:**

**As you can see, common Ratio is two. So, we’ll introduce you with one more trick here.**

Multiply the ratio by itself as many as there is total numbers in the series Subtract 1 from the product and multiply Result by the first number of series and after that divide result by the number 1 less than ratio.

Solution of above series by short trick.

Step 1 : 2*2*2*2= 16

Step 2 : 16-1= 15

Step 3 : 15*95= 1425

Step 4: 1425/1= 1425

So, Sum of our series is 1425.

Try above tricks on below exercise and let us know in case of any doubt:

This is all about the short-cuts of addition. In next chapter, we’ll introduce with Shortcuts in Multiplication. Stay with us for more updates

Good Luck.