import java.util.Scanner;
public class MathSequence {
public static Scanner newScanner = new Scanner(System.in);
	public static void main(String[] args) {


		  Scanner scanner = new Scanner(System.in);
	        while (true) {
	            System.out.println(CHOICEQUESTION);
	            int userResponse = scanner.nextInt();

	            while (!(userResponse == 1 || userResponse == 2 | userResponse == 3)) {

	                System.out.println(ERRORMESSAGE);
	                System.out.println(CHOICEQUESTION);
	                scanner.nextLine();
	                userResponse = scanner.nextInt();


	            }
	            if (userResponse == 1) {


	                System.out.println("Enter the first term in the arithmetic sequence: ");
	                int firstNumber = scanner.nextInt();
	                System.out.println("Enter the common difference in the arithmetic sequence:");
	                int commonDiffernce = scanner.nextInt();
	                System.out.println("Enter the number of terms in the arithmetic sequence: ");
	                int numTerms = scanner.nextInt();


	                int[] array = new int[numTerms];
	                array[0] = firstNumber;
	                int sum = array[0];
	                System.out.print("<" + array[0]);
	                for (int i = 1; i < numTerms; i++) {

	                    array[i] = array[i - 1] + commonDiffernce;
	                    sum = sum + array[i];

	                    System.out.print(", " + array[i]);
	                }
	                System.out.println(">");

	                System.out.println("Sum of the arithmetic sequence: " + sum);

	            }


	            else if (userResponse == 2) {


	                System.out.println("Enter the first term in the geometric sequence: ");
	                int firstNumber = scanner.nextInt();
	                System.out.println("Enter the common ratio in the geometric sequence:");
	                int commonRatio = scanner.nextInt();
	                System.out.println("Enter the number of terms in the geometric sequence: ");
	                int numTerms = scanner.nextInt();
	                int[] array = new int[numTerms];
	                array[0] = firstNumber;
	                int sum = array[0];
	                System.out.print("<" + array[0]);
	                for (int i = 1; i < numTerms; i++) {

	                    array[i] = array[i - 1] * commonRatio;
	                    sum = sum + array[i];

	                    System.out.print(", " + array[i]);
	                }
	                System.out.println(">");

	                System.out.println("Sum of the geometric sequence: " + sum);


	            } else if (userResponse == 3) {

	                int[] array = new int[10];

	                int count = 0;

	                while (true) {
	                    System.out.println("Enter a new number: ");

	                    array[count++] = scanner.nextInt();

	                    if (count == 10) {
	                        System.out.println("You have entered the maximum number of numbers!\n" +
	                                "We will start processing your sequence right away.");
	                        break;

	                    } else {
	                        System.out.println("You have entered " + count + " numbers ");
	                        System.out.println("You may still enter another " + (10 - count) + " numbers.");

	                        System.out.println("Would you like to enter another new number? (Y/N)");

	                                                                                 // Scanner.nextline()
	                        String continueGame = newScanner.nextLine();

	                        if (!(continueGame.equals("Y"))) {

	                            break;


	                        }
	                    }
	                }

	                if (count == 1) {

	                    System.out.println("Error: we cannot infer the common difference from a sequence of size one.");
	                } else {
	                    int commonDifference = array[1] - array[0];
	                    boolean isSequence = true;
	                    for (int i = 1; i < count - 1; i++) {


	                        if (array[i + 1] - array[i] != commonDifference) {

	                            isSequence = false;
	                            break;
	                        }


	                    }

	                    if (isSequence) {

	                        int sum = array[0];
	                        System.out.print("<" + array[0]);
	                        for (int i = 1; i < count; i++) {

	                            sum = sum + array[i];

	                            System.out.print(", " + array[i]);
	                        }
	                        System.out.println("> is an arithmetic sequence with\n" +
	                                "first term " + array[0] + " common difference " + commonDifference + " length " + count + " and sum " + sum);


	                    } else {
	                        System.out.print("<" + array[0]);
	                        for (int i = 1; i < count; i++) {


	                            System.out.print(", " + array[i]);
	                        }
	                        System.out.println("> is not an arithemtic sequence ");

	                    }
	                }
	            }

	            System.out.println("Do you want to play again? (Y/N)");
	scanner.nextLine();

	            String continueGame = scanner.nextLine();

	            if (!(continueGame.equals("Y"))) {

	                break;


	            }

	        }
System.out.println("Bye!");
	    }

	    private static String CHOICEQUESTION = "What kind of processing task would you like to perform? \n1: Generate an arithmetic sequence. \n2: Generate a geometric sequence. \n3: Determine an arithmetic sequence.";
	    private static String ERRORMESSAGE = "Error: task number must be 1, 2, or 3.";


	}