Posted by **Rachel** on Wednesday, October 12, 2011 at 7:14pm.

I understand how to use a calculator to write the decimal point using the golden ratio which is 1.618034 and the conjugate is -.618034. I also know that the relationship between the decimal expansions is that everything to the right of the decimal is the same except one is neg. and one is pos.

Now I have a problem. I have to use the Binet form to calculate the 20th Fib. number. I can use my decimals that I used in the problem above, but I am not sure how to do this. I have worked out the Fibonacci numbers and found that the 20th number is 6,765.

I could really use some help in understanding my problem.

- Fibonacci Numbers: Understand one part not another -
**MathMate**, Wednesday, October 12, 2011 at 11:30pm
You have correctly calculated the 20th fibonacci number as 6765. That's an excellent start.

To calculate any Fibonacci number without having to go through the recursive process (n times) is to use the Binet's formula.

To simiply things, two constants have been defined:

φ=(1+sqrt(5))/2, and

ψ=(1-sqrt(5))/2

then the nth Fibonacci number can be found with the following formula:

F(n)=(φ^n-ψ^n)/sqrt(5)

If your calculator does not have constants to store φ and ψ you can calculate directly as:

F(n)=(((1+√5)/2)^n-((1-√5)/2)^n)/√5

It should give 6765 if you put n=20.

## Answer This Question

## Related Questions

- Fibonacci Numbers - I posted the question several days ago and Mathmate helped ...
- Fibonacci numbers - I have been working on this question all day and can not ...
- maths! please help me it is an emergency!!!!!!!!!! - what is the fibonacci ...
- Fibonacci numbers - I have three problems to answer dealing with Fibonacci ...
- Math - Hi, I have to write a 2 page paper on any subject in math that interests ...
- Computer Science - MATLAB - One interesting property of a Fibonacci sequence is ...
- Computer Science - MATLAB - I guess it was skipped One interesting property of a...
- math - The Fibonacci sequence of numbers begins 1,1,2,3,5,8,13,21,34,55,…and ...
- algebra - In finding distance problems i understand the use of formula of d/rt ...
- Calculus - Oil is leaking out of a ruptured tanker at a rate of r = 19e^(2t) ...

More Related Questions