# Find Nth term of the series where each term differs by 6 and 2 alternately

• Last Updated : 05 Aug, 2022

Given a number N, the task is to find the Nth term of the series where each term differs by 6 and 2 alternately.
Examples:

Input: N = 6
Output: 24
Explanation:
The Nth term is 0 + 6 + 2 + 6 + 2 + 6 + 2 = 24
Input: N = 3
Output: 14
Explanation:
The Nth term is 0 + 6 + 2 + 6 = 14

Naive Approach: The idea is to iterate from 1 with an increment of 6 and 2 alternatively, till we reach the Nth term.
Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Function to find Nth term``void` `findNthTerm(``int` `N)``{``    ``int` `ans = 0;` `    ``// Iterate from 1 till Nth term``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``// Check if i is even and``        ``// then add 6``        ``if` `(i % 2 == 0) {``            ``ans = ans + 6;``        ``}` `        ``// Else add 2``        ``else` `{``            ``ans = ans + 2;``        ``}``    ``}` `    ``// Print ans``    ``cout << ans << endl;``}` `// Driver Code``int` `main()``{``    ``int` `N = 3;``    ``findNthTerm(N);``    ``return` `0;``}`

## Java

 `// Java program for the above approach``class` `GFG{`` ` `// Function to find Nth term``static` `void` `findNthTerm(``int` `N)``{``    ``int` `ans = ``0``;`` ` `    ``// Iterate from 1 till Nth term``    ``for` `(``int` `i = ``0``; i < N; i++) {`` ` `        ``// Check if i is even and``        ``// then add 6``        ``if` `(i % ``2` `== ``0``) {``            ``ans = ans + ``6``;``        ``}`` ` `        ``// Else add 2``        ``else` `{``            ``ans = ans + ``2``;``        ``}``    ``}`` ` `    ``// Print ans``    ``System.out.print(ans +``"\n"``);``}`` ` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `N = ``3``;``    ``findNthTerm(N);``}``}` `// This code is contributed by PrinciRaj1992`

## Python3

 `# Python3 program for the above approach` `# Function to find Nth term``def` `findNthTerm(N):``    ``ans ``=` `0` `    ``# Iterate from 1 till Nth term``    ``for` `i ``in` `range``(N):` `        ``# Check if i is even and``        ``# then add 6``        ``if` `(i ``%` `2` `=``=` `0``) :``            ``ans ``=` `ans ``+` `6``        `  `        ``# Else add 2``        ``else` `:``            ``ans ``=` `ans ``+` `2``        ` `    ``# Print ans``    ``print``(ans)`  `# Driver Code``if` `__name__``=``=``'__main__'``:` `    ``N ``=` `3``    ``findNthTerm(N)``    `  `# This code is contributed by AbhiThakur`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to find Nth term``static` `void` `findNthTerm(``int` `N)``{``    ``int` `ans = 0;` `    ``// Iterate from 1 till Nth term``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``// Check if i is even and``        ``// then add 6``        ``if` `(i % 2 == 0) {``            ``ans = ans + 6;``        ``}` `        ``// Else add 2``        ``else` `{``            ``ans = ans + 2;``        ``}``    ``}` `    ``// Print ans``    ``Console.Write(ans +``"\n"``);``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int` `N = 3;``    ``findNthTerm(N);``}``}` `// This code is contributed by AbhiThakur`

## Javascript

 ``

Output:

`14`

Time Complexity: O(N)

Auxiliary Space: O(1) as using constant variables

Efficient Approach: We can find the Nth term by using the below formula:

1. If N is Odd: The Nth term is given by (N/2 + 1)*6 + (N/2)*2.
2. If N is Even: The Nth term is given by (N/2)*6 + (N/2)*2.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Function to find Nth term``void` `findNthTerm(``int` `N)``{``    ``int` `ans;` `    ``// Check if N is even``    ``if` `(N % 2 == 0) {` `        ``// Formula for n is even``        ``ans = (N / 2) * 6``              ``+ (N / 2) * 2;``    ``}` `    ``// Check if N is odd``    ``else` `{``        ``// Formula for N is odd``        ``ans = (N / 2 + 1) * 6``              ``+ (N / 2) * 2;``    ``}` `    ``// Print ans``    ``cout << ans << endl;``}` `// Driver Code``int` `main()``{``    ``int` `N = 3;``    ``findNthTerm(N);``    ``return` `0;``}`

## Java

 `// Java program for the above approach`  `class` `GFG{`` ` `// Function to find Nth term``static` `void` `findNthTerm(``int` `N)``{``    ``int` `ans;`` ` `    ``// Check if N is even``    ``if` `(N % ``2` `== ``0``) {`` ` `        ``// Formula for n is even``        ``ans = (N / ``2``) * ``6``              ``+ (N / ``2``) * ``2``;``    ``}`` ` `    ``// Check if N is odd``    ``else` `{``        ``// Formula for N is odd``        ``ans = (N / ``2` `+ ``1``) * ``6``              ``+ (N / ``2``) * ``2``;``    ``}`` ` `    ``// Print ans``    ``System.out.print(ans +``"\n"``);``}`` ` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `N = ``3``;``    ``findNthTerm(N);``}``}` `// This code contributed by PrinciRaj1992`

## Python3

 `# Python3 program for the above approach` `# Function to find Nth term``def` `findNthTerm(N):``    ``ans ``=` `0``;` `    ``# Check if N is even``    ``if` `(N ``%` `2` `=``=` `0``):` `        ``# Formula for n is even``        ``ans ``=` `(N ``/``/` `2``) ``*` `6` `+` `(N ``/``/` `2``) ``*` `2``;``    ` `    ``# Check if N is odd``    ``else``:``        ` `        ``# Formula for N is odd``        ``ans ``=` `(N ``/``/` `2` `+` `1``) ``*` `6` `+` `(N ``/``/` `2``) ``*` `2``;``    ` `    ``# Print ans``    ``print``(ans);``    ` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``N ``=` `3``;``    ``findNthTerm(N);``    ` `# This code is contributed by Rajput-Ji`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{``  ` `// Function to find Nth term``static` `void` `findNthTerm(``int` `N)``{``    ``int` `ans;``  ` `    ``// Check if N is even``    ``if` `(N % 2 == 0) {``  ` `        ``// Formula for n is even``        ``ans = (N / 2) * 6``              ``+ (N / 2) * 2;``    ``}``  ` `    ``// Check if N is odd``    ``else` `{``        ``// Formula for N is odd``        ``ans = (N / 2 + 1) * 6``              ``+ (N / 2) * 2;``    ``}``  ` `    ``// Print ans``    ``Console.Write(ans +``"\n"``);``}``  ` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `N = 3;``    ``findNthTerm(N);``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output:

`14`

Time Complexity: O(1)

Auxiliary Space: O(1) since using constant variables

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