6-1) (Math: pentagonal numbers) A pentagonal number is defined as n(3n–1)/2 for n = 1, 2, . . ., and so on. Therefore, the first few numbers are 1, 5, 12, 22, . . . . Write a method with the following header that returns a pentagonal number: public static int getPentagonalNumber(int n) Write a test program that uses this method to display the first n pentagonal numbers with 10 numbers on each line, one space between each number, and the user entering the integer value for n.

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Explanation:

public class Exercise_06_01 {

/** Main Method */

public static void main(String[] args) {

 final int NUMBER_OF_PENTAGONALS = 100; // Display the first 100 pentagonals

 final int NUMBER_PER_LINE = 10; // Display 10 number per line

 // Display the first 100 pentagol numbers

 System.out.println("The first 100 pentagonal numbers, ten per line: ");

 for (int i = 1; i <= NUMBER_OF_PENTAGONALS; i++) {

 // Print ten numbers per line

 if (i % NUMBER_PER_LINE == 0)  

   System.out.printf("%7d\n", getPentagonalNumber(i));

 else

   System.out.printf("%7d", getPentagonalNumber(i));

 }

}

/** Return a pentagonal number */

public static int getPentagonalNumber(int n) {

 return (n * (3 * n - 1)) / 2;

}

}

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