I need to find f24. I know F23=28657 and f25=75025. I have figured out that F24 is 46368 using F(n)=F(n-1)+F(n-2).
My problme is asking me for two values of n for which Fn=n. I do not understand what it is asking.
Using the golden ratio, what if f24,f27,f29,f31,f34,f38,f40,f45,f48,f70?
As you said, f23=28657, but 23≠28657.
You need to find 2 values of n where fn=n.
f0=0 is one example. There are two more, and they are at the beginning of the sequence, so you must have gone past them a few times already.
There is only one Fn = n and that's n=1
The problem is asking you to find two values of n for which the Fibonacci number Fn is equal to n. In other words, you need to find two values of n such that when you plug in those values into the Fibonacci sequence equation F(n) = F(n-1) + F(n-2), the result is n.
To solve this problem, you can start by manually calculating the Fibonacci sequence until you find the matching values of n. Here's how you can do it:
1. Begin with the initial values of the Fibonacci sequence, F0 = 0 and F1 = 1.
2. Calculate the next term in the sequence using the Fibonacci sequence equation: F2 = F1 + F0 = 1 + 0 = 1.
3. Repeat the process to find the following terms in the sequence:
F3 = F2 + F1 = 1 + 1 = 2
F4 = F3 + F2 = 2 + 1 = 3
F5 = F4 + F3 = 3 + 2 = 5
F6 = F5 + F4 = 5 + 3 = 8
F7 = F6 + F5 = 8 + 5 = 13
F8 = F7 + F6 = 13 + 8 = 21
F9 = F8 + F7 = 21 + 13 = 34
F10 = F9 + F8 = 34 + 21 = 55
F11 = F10 + F9 = 55 + 34 = 89
F12 = F11 + F10 = 89 + 55 = 144
F13 = F12 + F11 = 144 + 89 = 233
F14 = F13 + F12 = 233 + 144 = 377
F15 = F14 + F13 = 377 + 233 = 610
F16 = F15 + F14 = 610 + 377 = 987
F17 = F16 + F15 = 987 + 610 = 1597
F18 = F17 + F16 = 1597 + 987 = 2584
F19 = F18 + F17 = 2584 + 1597 = 4181
F20 = F19 + F18 = 4181 + 2584 = 6765
F21 = F20 + F19 = 6765 + 4181 = 10946
F22 = F21 + F20 = 10946 + 6765 = 17711
F23 = F22 + F21 = 17711 + 10946 = 28657
F24 = F23 + F22 = 28657 + 17711 = 46368
Now, to find the values of n for which Fn=n, you can check which terms in the sequence have the same value as their corresponding index. In this case, there are two such values:
- n=0, F0=0
- n=1, F1=1
So, the two values of n for which Fn=n are 0 and 1.
Bzzt! Just start a list
n = 1 2 3 4 5 6
Fn = 1 1 2 3 5 8
F1 = 1
F5 = 5