Wednesday

April 16, 2014

April 16, 2014

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

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 11:30pmYou 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.

**Related Questions**

Fibonacci Numbers - I posted the question several days ago and Mathmate helped ...

Fibonacci numbers - I have three problems to answer dealing with Fibonacci ...

Maths - I have a summation formula for Fibonacci numbers. n (SUM)F(2i)=F(2n+1)-1...

Math - F25= 75,025 and F26= 121,393 where Fn is the nth term in the Fibonacci ...

Fibonacci Numbers - I need to find f24. I know F23=28657 and f25=75025. I have ...

math - There is no function equation for the Fibonacci numbers, you have to use ...

Linerar Equations in 2 Variables - Complete the ordered pair for the equation y...

Colelge Math (Fibonacci) - "Start with a pair of rabbits, (one male and one ...

math - I understand the Fibonacci Sequence (the simplified version). But how is ...

math - How many two digit numbers are there in base 5. I really don't understand...