ADDING A SERIES OF NUMBERS WITH A COMMON DIFFERENCE

 

5)

ADDING A SERIES OF NUMBERS WITH A COMMON DIFFERENCE

Sometimes it is necessary to add a group of numbers that have a common difference. No matter what the common differenc e is and no matter how many numbers are being added, only one addition, multiplication, and division will be necessary to obtain the answer.

Rule:

           (Add the smallest number to the largest number, multiply the sum by the amount of numbers in the group, and divide by 2)

As an example, let us find the sum of the following numbers

87, 91, 95, 99, and 103

Notice that the difcrence between adjacent numbers is

always 4. This short-cut method can therefore be us ed.

Add the smallest number, 87, to the largest number, 103.

Multiply the sum, 190, by 5, since there are five numbers

in the group.

190 x 5= 950 

Divide by 2 to obtain the answer.

950 / 2 = 475 Answer

Thus 87+ 91 95 + 99 +103 = 475.

(Naturally, this is exactly the same as the rule in Short

Cut 1, because there we were simply adding a series of

numbers with a common difference of one. So, for casc of

remembering, you can combine Short Cuts 1 and 5.)