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Program to find N-th term of series 1, 2, 11, 12, 21….
• Last Updated : 25 Oct, 2018

Given a number N, the task is to find the Nth term of the series:

1, 2, 11, 12, 21…

Examples:

```Input : N = 2
Output : 2

Input : N = 5
Output : 21
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:
The idea is based on the fact that the value of the last digit alternates in the series. For example, if the last digit of ith number is 1, then the last digit of (i-1)th and (i+1)th numbers must be 2.

Therefore, Create an array of size (n+1) and push 1 and 2(These two are always first two elements of series) to it.

Therefore the ith term of the array is:
1) If i is odd,
arr[i] = arr[i/2]*10 + 1;
2) If i is even,
arr[i] = arr[(i/2)-1]*10 + 2;

At last return arr[n].

Below is the implementation of the above idea:

## C++

 `// C++ program to find``// the N-th term in the series``// 1, 2, 11, 12, 21...`` ` `#include ``using` `namespace` `std;`` ` `// Function to find N-th number in series``int` `printNthElement(``int` `N)``{``    ``// create an array of size (N+1)``    ``int` `arr[N + 1];``    ``arr = 1;``    ``arr = 2;`` ` `    ``for` `(``int` `i = 3; i <= N; i++) {``        ``// If i is odd``        ``if` `(i % 2 != 0) {`` ` `            ``arr[i] = arr[i / 2] * 10 + 1;``        ``}``        ``else` `{`` ` `            ``arr[i] = arr[(i / 2) - 1] * 10 + 2;``        ``}``    ``}``    ``return` `arr[N];``}`` ` `// Driver code``int` `main()``{`` ` `    ``// Get N``    ``int` `N = 5;`` ` `    ``// Get Nth term``    ``cout << printNthElement(N);`` ` `    ``return` `0;``}`

## Java

 `// Java program to find``// the N-th term in the series``// 1, 2, 11, 12, 21...`` ` `class` `FindNth {`` ` `    ``// Function to find n-th number in series``    ``static` `int` `printNthElement(``int` `n)``    ``{``        ``// create an array of size (n+1)``        ``int` `arr[] = ``new` `int``[n + ``1``];``        ``arr[``1``] = ``1``;``        ``arr[``2``] = ``2``;`` ` `        ``for` `(``int` `i = ``3``; i <= n; i++) {``            ``// If i is odd``            ``if` `(i % ``2` `!= ``0``)``                ``arr[i] = arr[i / ``2``] * ``10` `+ ``1``;``            ``else``                ``arr[i] = arr[(i / ``2``) - ``1``] * ``10` `+ ``2``;``        ``}``        ``return` `arr[n];``    ``}`` ` `    ``// main function``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `n = ``5``;`` ` `        ``System.out.println(printNthElement(n));``    ``}``}`

## Python3

 `# Python3 program to find``# the N-th term in the series``# 1, 2, 11, 12, 21...`` ` `# Return n-th number in series``def` `printNthElement(n) :  ``         ` `    ``# create an array of size (n + 1)  ``    ``arr ``=``[``0``] ``*` `(n ``+` `1``);  ``    ``arr[``1``] ``=` `1``    ``arr[``2``] ``=` `2``     ` `    ``for` `i ``in` `range``(``3``, n ``+` `1``) :  ``        ``# If i is odd  ``        ``if` `(i ``%` `2` `!``=` `0``) :  ``            ``arr[i] ``=` `arr[i ``/``/` `2``] ``*` `10` `+` `1``        ``else` `:  ``            ``arr[i] ``=` `arr[(i ``/``/` `2``) ``-` `1``] ``*` `10` `+` `2``         ` `    ``return` `arr[n]  ``         ` `# Driver code  ``n ``=` `5``print``(printNthElement(n))  `

## C#

 `// C# program to find``// the N-th term in the series``// 1, 2, 11, 12, 21...``using` `System;`` ` `class` `GFG ``{`` ` `// Function to find n-th``// number in series``static` `int` `printNthElement(``int` `n)``{``    ``// create an array of size (n+1)``    ``int` `[]arr = ``new` `int``[n + 1];``    ``arr = 1;``    ``arr = 2;`` ` `    ``for` `(``int` `i = 3; i <= n; i++)``    ``{``        ``// If i is odd``        ``if` `(i % 2 != 0)``            ``arr[i] = arr[i / 2] * 10 + 1;``        ``else``            ``arr[i] = arr[(i / 2) - 1] * 10 + 2;``    ``}``    ``return` `arr[n];``}`` ` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `n = 5;`` ` `    ``Console.WriteLine(printNthElement(n));``}``}`` ` `// This code is contributed``// by inder_verma`

## PHP

 ``
Output:
```21
```

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