Calculate the total items used, if for every x items used, you get one additional item to use
I managed to create another algorithm that produces the same results, this algorithm iteration seems to be more efficient so it will perform better. 

Consider startingTotalItems as x and newItemInterval as y.

Using while loop:

public static int TotalItems(int x, int y)
{
    int sum = 0; 
    while (x &gt;= y) 
    {  
        int remainder = x % y; 
        int quotient = x / y;
        sum += (x - remainder); 
        x = remainder +  quotient;
    } 
    return sum + x;
} 


Using recursive method:

public static int TotalItems(int x, int y)
{
    if(x &lt; y)
    {
        return x;
    }
    int remainder = x % y;
    int quotient = x / y;
    return x - remainder + TotalItems(remainder +  quotient, y);
}


How does it work? 
Let's assume that x is the amount of items we are holding now.
For every x bigger than or equal to y we will add to the sum x without the remainder of x divided by y, let's consider that these are the items we've used during this turn.  
Now we still have the remainder that we haven't used yet but we need to remember the we've got more items while using the previous items, the amount of items we've got is the quotient of x divided by y, so now x should be the quotient plus the remainder. 
We will repeat this procedure until x is less than y in this case we know that we will not get any more items so all we have left to do is to add x to the sum, break the procedure and return the result.