I don't understand the sigma notation and for loop

Question

I have the book saying that

and says that this is equivalent to saying

Answer 1

I created this while loop illustrating sigma notation elements in detail.

//Illustrates how loops are similar to Sigmas in Math
//This is equal to:
//100
//Sigma x+5
//x=1

package justscratch;

public class SigmaCalculatorWhileLoop {
    private static int initial = 0; //Initial. Will increment by one until it reaches limit.
    private static final int limit = 100; //Limit
    private static final int incr = 5; //Number Incremental
    private static int pass = 0; //Will illustrate the current pass
    private static int tempAnswer = 0; //The previous sum
    private static int finalAnswer = 0; //The current sum

    public static void main(String[] args) {
        while(pass<=limit) {
            System.out.println("Pass: " + pass); //Prints out current Loop Pass
            System.out.println(tempAnswer); //Prints out the sequences generated by each iteration from the "sigma"
            tempAnswer = initial + incr; //Creates a new increased sequence until the limit is reached
            finalAnswer = tempAnswer + finalAnswer; //Adds the previous sequence with the current sequence
            pass++; //Increases the current pass
            initial++; //The initial value will increase by 1 until it reaches it's limit
        }
        System.out.println("Sigma Answer: " + finalAnswer); //Prints the final sum of the "Sigma"
    }
}

In summary, this app will simulate the sigma 100 Σ n+5 n=0. The app works by generating a previous and current sequence based on the sigma, and adding these both the current & previous sequence together until the sigma limit is reached to calculate the total returned by the sigma. So the sequences {5+6+7+8+9+10,11+. . . . 105} will be added altogether.