Math Delights

From Mathemagic by Don Fraser, page 26 and Mathemagical Showtime! by Carl M Sherrill, page 99

Use the following trick to quickly compute the sum of a list of 10 numbers (a Fibonocci sequence — visit etereaestudios.com/docs_html/nbyn_htm/movie_index.htm to see a movie inspired by Fibonacci numbers in nature and geometry).

1. Create your own Fibonacci sequence of numbers as follows:
   • Draw 10 short lines on a paper, one below the other.
   • Select 2 whole numbers between 0 and 7 and write them down on the 1st and 2nd lines.
   • Add the 2 numbers and write the sum on the 3rd line.
   • Add the 2nd and 3rd numbers and write the sum on the 4th line.
   • Continue adding the last 2 numbers and writing down their sum on the line below the last number in your list, until you have a list of 10 numbers.
2. Challenge someone to a race of computing the sum of the 10 numbers.
3. Compute the sum quickly in your head by multiplying the 7th number from the top by 11. (For a shortcut, visit mathdelights.org//delights/6-magic/36-multiplying-by-11-quickly.)

Here are two examples and a third empty column where you can make your own Fibonacci sequence:

Why can you get the sum by multiplying the 7th number by 11? If the 1st number in the list had a value of a and the 2nd number in the list had a value of b, what would be the value of the 7th number in terms of a and b and what would be the total?

If you need a hint, click here.