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Published on February 11th, 2013 In category Education | Maths

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# Tricks for adding sequence of numbers

A sequence of numbers can be represented as say 44, 45, 46, 47, 48, 49, 50, 51, 52. In this sequence we have smallest number as 44 and largest number as 52. There are in 9 numbers in this sequence. There are other type of sequence number as well. 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 in this sequence we have smallest number as 4 and biggest number as 22. Similarly there can be other sequence as well like 7, 14, 21,, 28, 35 etc, here the numbers are increasing by 7 each time. or we can have sequence such as 3, 9, 27, 81, 243 where the numbers is 3 time of preceding number.

The numbers step up in sequence of 2’s. If we need to add all these numbers it can be a quite a task.

There is a very simple trick to do all this calculations

The trick is as follows: Let take the sequence 44, 45, 46, 47, 48, 49, 50, 51, 52 for ex. There are 9 numbers in this sequence.

How did we get numbers in this sequence first by counting ????? or by subratracting largest number to smallest number and then add 1 (Why?) because while subtracting we take away the smaller number so add 1 (52-44+1) = 9

First add smaller and bigger number 44 + 52 = 96 multiply it by 9 = 96 x 9 = (100 – 4) x 9 = 900 -36 = 864 then divide by 2

Rule: Add the smallest and largert number in the group and multiply with the amount of numbers in the group and divide the result by 2

To add the sequence of numbers starting from 1 to any number. for ex. Adding the sequence of numbers from say 1 to 99. This case add the 1 to largest number (99) multiply with amount of numbers 99, this equals to 9900 and then divide by 2 which equals to 4950.

RuleAdd 1 to the largest numbers and multiply with the amount of the numbers and then divide by 2