Write a Program Average of Array in Java- Technology369kk

 Average of Array

Program: 

// Q6. WAP where use SUm of Average numbers

class ArrayArray{

    public static void main(String arg[]){

        // define an array

        int[] numbers = new int [] {10,20,30,40,50};

        // calculate sum of all array elements

        int sum =0;

       

        for (int i= 0; i< numbers.length; i++){

            sum = sum + numbers[i];

        }

        // calculate average value

        double average = sum/numbers.length;

        System.out.println("Average value of array elements is:"+average);

    }

}

Explanation :  

• I am using in this program fast: - sum of natural numbers formal 

The formula for the sum of the first $n$ natural numbers is:

                                        Sn​=n(n+1)/2

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Explanation:

• Natural numbers: These are the counting numbers starting from 1 (i.e., $1, 2, 3, \dots, n$).
• Formula Derivation:
• If we sum the first $n$ natural numbers: $$S_n = 1 + 2 + 3 + \dots + n$$
• Pairing the terms from start and end: $$(1 + n), (2 + (n-1)), (3 + (n-2)), \dots$$ Each pair sums to $n+1$, and there are $\frac{n}{2}$ pairs (if $n$ is even). 
• If $n$ is odd, the middle term will be unpaired, but the formula still holds.

Example:

For $n = 5$:

$$S_5 = \frac{5(5+1)}{2} = \frac{5 \times 6}{2} = 15$$

Verification:-   1+2+3+4+5= 15