How are we able to calculate specific numbers in the Fibonacci Sequence?

Question

I was reading up on the Fibonacci Sequence, $\ ext {{1,1,2,3,5,8,13,....}}$ when I've noticed some were able to calculate specific numbers. So far I've only figured out creating an array and counting to the value, which is incredibly simple, but I reckon I can't find any formula for calculating a Fibonacci number based on it's position. Is there a way to do this? If so, how are we able to apply these formulas to arrays?

Answer 1

using namespace std;

#include <iostream>

#define MAX (47) //MAX that can be stored before overflow

//returns the Nth fibonacci number

long Fib(int n)

{

int iReturn=-1;

if ((n==1) || (n==2))

{

iReturn=1;

}

else if (n>1)

{

iReturn = Fib(n-1)+ Fib(n-2);

}

return(iReturn);

}

int main()

{

long A[MAX]; //stores the fibonacci numbers

// is 1-based, so the array index corresponds

// directly with the position of the fibonacci #

//1,1,2,3,5,6

cout << Fib(6) << endl; //Fib(6) = 8

//.... and here is your array

A[1]=A[2] = 1;

for (int iLoop=3; iLoop<MAX; iLoop++)

{

A[iLoop] = A[iLoop-1]+A[iLoop-2];

cout << A[iLoop] << endl;

}

}