Shortcut for Addition of Consecutive Numbers

In this post I’ll share with you a useful shortcut maths trick for “finding out the sum of consecutive numbers”. For example, this trick I am talking about can help you in finding the sum of all the numbers from 23 to 31 or any other set of numbers.

Shortcut Addition Trick

Add the smallest number to the largest number of the given set of consecutive numbers. Then multiply the result by the number of numbers in the set. Finally divide the result by two.

Solving the above example, let’s find: 23+24+25+26+27+28+29+30+31

Step 1: Add the smallest and the largest number from the above set of numbers:

23 + 31 = 54

Step 2: Multiply the result by the number of numbers in the above set. In the above set there are 9 numbers from 23 to 31.

Therefore, multiply 54 by 9

54 x 9 = 486

Step 3: Finally, divide the above result by 2

486/2 = 243

Hence, 23+24+……..+31 = 243

So now, since you know this simple calculation trick, you don’t have to add up each number individually to get the answer. With a little practice, this trick might become a good tool to save lot of your time. In adding numbers the biggest problem faced is the issue of carryover. Check out how carryover in addition can be avoided to make any addition much simpler.

If you want to suggest some additions or modification in the above method, feel free to post your suggestion as comment below. To learn another shortcut addition trick, read this post

I am glad to include the suggestions posted as comment below, for the benefit of everyone.

Suggestion by Sagar Shah -

“If there are odd number of terms then multiply the middle term with number of terms and you get the answer.

We will take the same example. 23+24+25+26+27+28+29+30+31

Here the middle term = 27 and the num of terms is 9.
Therefore the answer is 9*27 = 243

If there are even number of terms then take the mean of the two middle terms
eg 23+24+25+26+27+28+29+30

Here there are 8 terms and the two middle terms are 26 and 27. So mean is 26.5. Multiply it with num of terms i.e 8
Solution is 26.5 * 8 = 212″

One very simple formula is used to deduce this addition shortcut. If you could identify that, post it as comment below.

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