To Solve Number System Problems Using Java Program…Part-5.

Hi guys, In this article, We will discuss Odd Numbers, related mathematical problems and Programming way using Java.

Formulas:-

Odd Numbers:-

1. The sum of the first ’N’ Odd Numbers is N².
2. The sum of the ’N’ Odd Numbers is [(n(a+l))/2].

Where n=((Last term-First term)/Difference of CN)+1,n is No. of Numbers, a is the first term, l is the last term, and CN is a Consecutive Number.

Problems:-

Q. Find the sum of the first 30 odd numbers.

Ans. n²=>30²=>900.

In programming way.

import java.util.Scanner;

public class SumOfFirstOddNums {

 public static void main(String[] args) {
  Scanner scanner = new Scanner(System.in);
  System.out.println("Enter any Natural Number:");
  int natural_number = scanner.nextInt();//30
  int result = 0;
  for (int i = 0; i <=2*natural_number; i++) {
   if (i % 2 != 0) {
    result = result + i;
   }
  }
  System.out.println(result+" is the sum of the first "+natural_number+" odd numbers.");
   //result=900.
 }

}

output:
Enter any Natural Number:
30
900 is the sum of the first 30 odd numbers.

Q. Find the sum of odd numbers up to 15.

Ans.n=13, n²=13²=>169.

In Programming way.

import java.util.Scanner;

public class SumOfOddNumsUpto {

 public static void main(String[] args) {
  Scanner scanner = new Scanner(System.in);
  System.out.println("Enter any Natural Number:");
  int natural_number = scanner.nextInt();//15
  int result = 0;
  for (int i = 1; i < 2 * natural_number-1; i++) {
   if (i % 2 != 0) {
    result = result + i;
   }
  }
  System.out.println(result+" the sum of odd numbers up to "+natural_number);
  //result=196
 }

}

output:
Enter any Natural Number:
15
196 the sum of odd numbers up to 15

Q. Find the sum of odd numbers from 25 to 75.

Ans. First term=25, Last term=75 => n=((last term-first term)/Diff of CN)+1 =>((75–25)/2)+1 => (50/2)+1=19. n=26.

N=(n(a+l))/2 where n=26, a=25, l=75. =>(26(25+75))/2 =>(26(100))/2 =>13(100) =>1300.

In Programming way.

import java.util.Scanner;

public class SumofOddNums {
 public static void main(String[] args) {
  Scanner scanner = new Scanner(System.in);
  System.out.println("Enter First Natural Number:");
  int natural_number1 = scanner.nextInt();//25
  int result1 = 0;
  for (int i = 0; i <natural_number1; i++) {
   if (i % 2 != 0) {
    result1 = result1 + i;
   }
  }
  System.out.println("Enter second Natural Number:");
  int natural_number2 = scanner.nextInt();//75
  int result2 = 0;
  for (int i = 0; i <=natural_number2; i++) {
   if (i % 2 != 0) {
    result2 = result2 + i;
   }
  }
  int N=result2-result1;
  System.out.println(N+" is the sum of the odd numbers from "+natural_number1+" to "+natural_number2);//1300

 }

}

output:
Enter any First Natural Number:
25
Enter any Second Natural Number:
75
1300 is the sum of the odd numbers from 25 to 75.

Conclusion:-

Continue in the next article. Thanks for reading Please Follow Ram.