There is no function equation for the Fibonacci numbers, you have to use a Recursion formula.
F(n) = F(n-1) + F(n-2) for n>2 and F(1)=1, F(2)=1
what is the equation for the fibonacci sequence
Actually, there are a number of closed forms for Fn, but they are usually complicated. For example, Fn =
floor((n-1)/2)
∑ (n-k-1)Ck
k=0
where nCk is the combinations of n things k at a time
or
((1+√5)^n - (1-√5)^n)/(2^n √5)
The equation for the Fibonacci sequence is a recursive formula, as you mentioned. It relates each term in the sequence to the two preceding terms.
The formula is:
F(n) = F(n-1) + F(n-2)
where F(n) represents the nth term in the Fibonacci sequence. To use this formula, you need to know the values of the two previous terms, F(n-1) and F(n-2).
Additionally, the base cases for the Fibonacci sequence are F(1) = 1 and F(2) = 1. These are necessary to start the sequence.
To find a specific term in the Fibonacci sequence, you can start with the base cases and use the recursive formula to calculate subsequent terms. For example, to find F(5):
F(5) = F(4) + F(3)
= (F(3) + F(2)) + (F(2) + F(1))
= [(F(2) + F(1)) + F(2)] + [F(2) + F(1)]
= [1 + 1] + [1 + 1]
= 3 + 2
= 5
Therefore, F(5) is equal to 5 in the Fibonacci sequence.