Interesting Patterns

A) For each Fibonacci Number- Relation to adding ALL the previous numbers:

Fn= Fibonacci Number, All previous numbers added together

F1= 1, 1

F2= 1, 1

F3= 2, 2

F4= 3, 4

F5= 5, 7

F6= 8, 12

F7= 13, 20

F8= 21, 33

F9= 34, 54

F10= 55, 88

Pattern: When you add all the previous numbers together it is -1 of the next Fibonacci number!

B) Adding alternative Fibonacci Numbers

F0 + F2 = 0 + 1 = 1
F1 + F3 = 1 + 2 = 3
F2 + F4 = 1 + 3 = 4
F3 + F5 = 2 + 5 = 7
F4 +F6 = 3 + 8 = 11
F5+F7= 5 + 13 = 18

Pattern: The sum of the alternating fibonacci numbers plus the following sum is equal to the third sum (e.g. F0+F2=x; F1+F3=y; F2+F4= x+y)!