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August 29, 2014

August 29, 2014

Posted by **Jennifer** on Sunday, October 2, 2011 at 5:05pm.

1. Fibonacci numbers can not be used more than once. Find sums for numbers 75 and 40. 2+5+13+21+34=75

1+5+13+21=40

2. Writing the last equation in the Fibonacci

1=2-1

1+1=3-1

1+1+2=5-1

1+1+2+3=8-1

1+1+2+3+5=13-1

**1+1+2+3+5+8=21-1

*************************

1=1^2

1-1=-1^2

1-2+5=2^4

1-2+5-13=-3^2

1-2+5-13+34=5^2

**1-2+5-13+34-89=-8^2

This is the one I am completely lost on

3. Choose any term of the Lucas sequence other than the first and square it

1,3,4,7,11,18,29,47,76,123

Then multiply the terms immediately before and after the one you chose. Subtract the smaller result from the larger. Repeat this procedure two more times starting with different terms. Then make a conjecture about the result of the procedure.

I think I need to

3^2=9

9x1=3 9x4=36

36-3=33

*************************

4^2=16

16x3= 48 16x7=112

112-48=64

*************************

7^2=49

49x4=196 49x11=539

539-196=343

*************************

I do not know if this is correct or how to write a conjecture with the results. Appreciate all help

- Fibonacci numbers -
**bobpursley**, Sunday, October 2, 2011 at 5:24pm1,3,4,7,11,18,29,47,76,123

Pick number: 4, square it 16

then 3x7=21, 21-16=5

Pick number: 11, square it 121

then 7x18=126, 126-121= 5

pick number 47: square it 2209

then 29x76=2204, 2209-2204= 5

first two are correct.

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