The following program demonstrates how to Display the nth Number in a Sequence in Java.

At first, this program generates a series up to the given number of terms. Then, it returns the nth number in the series. There are four inputs – x1, x2, x3, and x4. Further, x1, x2, and x3 are the three terms in the series. Whereas, x4 represents n. The following conditions should satisfy:

  1. x1<x2<x3
  2. Let d be the next element after x3. So, d-x3 should be the same as x2-x1.
  3. Let e be the next element of d., so, e-d should be equal to x3-x2.

For example, let x=1, x2=3, x3=6, x4=17. So, the 17th number in the series should be returned. Therefore, the series will be

1 3 6 8 11 13 16 18 21 23 26 28 31 33 36 38 41. So, the 17th element is 41. Also, x2-x1=2, and x3-x2=3.

public class Sequences
{
	public static void main(String[] args)
	{
		System.out.println(firstSequence(1, 3, 6, 17));
		System.out.println(firstSequence(5, -2, -4, 14));
	}
	public static int firstSequence(int a, int b, int c, int N)
	{
		int next=0, t1, t2, t3, diff1, diff2;
		t1=a; t2=b; t3=c;
		diff1=b-a;
		diff2=c-b;
		System.out.print(a+" "+b+" "+c+" ");
		for(int i=4;i<=N;i++)
		{
			if(i%2==0) 
			{
				next=t3+diff1;
				t1=t2;
				t2=t3;
				t3=next;
			}
			else
			{
				next=t3+diff2;
				t1=t2;
				t2=t3;
				t3=next;
			}
			System.out.print(next+" ");
		}
		System.out.println();
		return next;
	}

}

Output

Display the nth Number in a Series in Java
A Program to Display the nth Number in a Series in Java

Further Reading

Java Practice Exercise

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