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

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

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

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 `

Output:

```14
```

Time Complexity: O(N)

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 `

Output:

```14
```

Time Complexity: O(1)

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