How do you use the equation for a fibonacci sequence?

Question

the equation for the fibonacci sequence is F(n)=F(n-1)+F(n-2), when n>1. Yet when i try to solve for known numbers in the sequence i don't get the next number. what am i doing wrong? n is the variable and F would be the next number in the sequence right?

Answer 1

F(n)=F(n-1)+F(n-2), where F(0) = 0 and F(1) = 1
n= 2
F(2) = F(2-1) + F(2-2)
F(2) = F(1) + F(0)
F(2) = 1 + 0 = 1
n = 3
F(3) = F(3-1) + F(3-2)
F(3) = F(2) + F(1)
F(3) = 1 + 1
F(3) = 2
n = 4
F(4) = F(4-1) + F(4-2)
F(4) = F(3) + F(2)
F(4) = 2 + 1
F(4) = 3
n = 5
F(5) = F(4) + F(3)
F(5) = 3 + 2
F(5) = 5

Answer 2

The sequence is: 1, 1, 2, 3, 5, 8, 13, 21, ...

How would you describe that sequence in English? You would say, "Every element in the sequence is equal to the sum of the element immediately prior and two elements prior."

That is what the equation says. The equation is the DEFINITION of the sequence.

In the notation F(n), F stands for Fibonacci, so

F(2) means "the second number in the Fibonacci sequence"
F(3) means "the third number in the Fibonacci sequence"

Here is the translation of the equation into English:

F(n) means any element of the sequence in which we are interested.
F(n-1) means the prior element.
F(n-2) means two elements prior.

So, just translating the English into math notation:

F(n) = F(n-1) + F(n-2)

If your computations don't produce the correct results, show me your computation and I'll show you where you are making your error.

There doesn't seem to be any formula for finding, say, the 80th Fibonacci number, except by saying it is the sum of the 79th and the 78th.

Answer 3

No, it's right, except that F() isn't a function. It's a list. So if the list's name was "t", then it would be as follows:

t(n) = t(n-1) + t(n-2)

For example, take t(7). In the Fibonacci sequence, this is 13. Then try adding t(n-1) and t(n-2), or 8 and 5. This makes 13. You're doing it right, but you're misinterpreting F().

Answer 4

Evolution believes that regardless of trait enables a specie stay to tell the story is the trait which will stick around. The series is taken into consideration one of the terrific way for species to strengthen seeing that nature do tend to take the path with least resistance. i do no longer see how this conflicts with evolution. in actuality, on account this is purely contemporary in some species and not others is evidence that no longer each thing become created out of the comparable mould. whether this is, as you declare, to be God's variety, then what do you call those that did no longer undergo the sequency?

Answer 5

Actually, there is a closed form expression for the Nth Fibonacci number. It is:

((1 + sqrt (5)) ^N - (1 - sqrt (5)) ^N) / (2^N * sqrt (5))

Answer 6

math girl, solving it algebraicly is what i did at first but it does not give you the numbers in the known sequence. superrobotz, your description makes sense but you would have to know the values for each place in the sequence to get it to add up- which it would. is that all its for? double checking not finding the next number in the sequence?