"Sum" More Quick Tricks

Sometimes, my students think, I am a magician who pulls answers out of a hat.  Over the years, I have learned that mathematicians are ingenious people who are always looking for quick and easy ways to do things.  Maybe that's why we now have graphing calculators and computer programs to figure taxes.

I have a friend who teaches math on the college level in North Carolina.  In fact, we have been friends since 6th grade, but that's another story.  When she read my posting of May 10th, she shared another trick for quickly finding a sum.  Her trick has to do with a sequence that begins with any number, with any number of terms as long as they are separated by the same amount.  For instance, the series below is a six number sequence with a difference of two between each number.

Here is what you do to quickly to find the sum.  Add the first and last terms.  5 + 15 = 20.  Now multiply by the number of terms which in this case is 6.  20 x 6 = 120   Finally, divide by 2.  So, mentally this is what it would look like.

Now, how many of you went back to add up 5 + 7 + 9 + 11 + 13 + 15?  Did you get the answer of  60?  Isn't it amazing!?!  Maybe math teachers are magicians after all!

   

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