Chapter 6, Problem 6.1PE

(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)

For example, getPentagonal Number (1) returns 1 and getPentagonalNumber(2) returns 5. Write a test program that uses this method to display the first 100 pentagonal numbers with 10 numbers on each line. Use the %7d format to display each number.

Program Plan Intro

Program Plan:

• Declare the class “Penta”
• Definition for main class
  • Use for loop to iterate the variable “j” equals to “100”.
  • Check whether “j” mod “10” equals to 0.
    • Call the method “getPentagonalNumber()”.
  • Otherwise, call the method “getPentagonalNumber()” concatenate with space.
• Method definition for “getPentagonalNumber()”
  • Return “n * (3 * n - 1) / 2”.

Program Description Answer

Program to display first 100 pentagonal numbers with 10 numbers on each line using the method “getPentagonalNumber ()”

Explanation of Solution

Program:

//Definition for class "Penta"

public class Penta

{

//Definition for main class

public static void main(String[] args)

{

//For loop to iterate the variable

for (int j = 1; j <= 100; j++)

//Check whether the variable "j" mod 10 equals to "0"

if (j % 10 == 0)

//Call the method "getPentagonalNumber"

System.out.println(getPentagonalNumber(j));

else

//Call the method "getPentagonalNumber"

System.out.print(getPentagonalNumber(j) + " ");

}

//Method definition for "getPentagonalNumber"

public static int getPentagonalNumber(int n)

{

//Return the result

return n * (3 * n - 1) / 2;

}

}

Sample Output

1 5 12 22 35 51 70 92 117 145

176 210 247 287 330 376 425 477 532 590

651 715 782 852 925 1001 1080 1162 1247 1335

1426 1520 1617 1717 1820 1926 2035 2147 2262 2380

2501 2625 2752 2882 3015 3151 3290 3432 3577 3725

3876 4030 4187 4347 4510 4676 4845 5017 5192 5370

5551 5735 5922 6112 6305 6501 6700 6902 7107 7315

7526 7740 7957 8177 8400 8626 8855 9087 9322 9560

9801 10045 10292 10542 10795 11051 11310 11572 11837 12105

12376 12650 12927 13207 13490 13776 14065 14357 14652 14950