Fibonacci sequence in Javascript

When you are reasoning about the code, you make the jump from fib[3] = fib[2] + fib[1] to fib[3] = fib[3]. This happens to be a transformation that results in a correct statement, but it is not how it works. This code is adding the value at index 2 to the value at index 1. That is not the same as taking the value at index 3. The way this reasoning should work is as follows:

You start with fib = [0, 1]. Then in the first iteration of the loop you have fib[2] = fib[1] + fib[0]. This means that you add the value at index 0 (which happens to be 0) to the value at index 1 (which happens to be 1) to get the value that you put at the end of the array (1). Then in the second iteration, you do a similar thing, adding the value at index 1 (still 1) to the value at index 2 (also 1) to get 2, which goes at the end of the array. This continues, and at each iteration you add together the last two values in the array to get the next value.

In JavaScript, when using an array like fib, fib[i] refers to the ith value in this array, counting from 0. So fib[0] is the first element in the array, fib[1] is the second element in the array, and so on.

fib[ 3 ] = fib[ 3 - 1 ] + fib[ 3 - 2 ];  
fib[ 3 ] = fib[ 2 ] + fib[ 1 ]; 
fib[ 3 ] = fib[ 3 ];

You are adding the indexes up not the value in the array the index points to

fib[ 3 ] = fib[ 3 - 1 ] + fib[ 3 - 2 ];  
fib[ 3 ] = fib[ 2 ] + fib[ 1 ]; 
fib[ 3 ] = 1 + 1;

[0,1,1,2]

fib[0] = 0
fib[1] = 1
fib[2] = 1
fib[3] will equal 2

So next iteration

fib[4] = fib[4-1] +fib[4-2]
fib[4] = fib[3] + fib[2]
fib[4] = 1 + 2
fib[4] = 3