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# Program for N-th term of Arithmetic Progression series

Given first term (a), common difference (d) and a integer N of the Arithmetic Progression series, the task is to find Nthterm of the series.
Examples :

```Input : a = 2 d = 1 N = 5
Output :
The 5th term of the series is : 6

Input : a = 5 d = 2 N = 10
Output :
The 10th term of the series is : 23```

Approach:

We know the Arithmetic Progression series is like = 2, 5, 8, 11, 14 …. …
In this series 2 is the stating term of the series .
Common difference = 5 – 2 = 3 (Difference common in the series).
so we can write the series as :
t1 = a1
t2 = a1 + (2-1) * d
t3 = a1 + (3-1) * d

tN = a1 + (N-1) * d

To find the Nth term in the Arithmetic Progression series we use the simple formula .

`TN = a1 + (N-1) * d`

## C++

 `// CPP Program to find nth term of``// Arithmetic progression``#include ``using` `namespace` `std;` `int` `Nth_of_AP(``int` `a, ``int` `d, ``int` `N)``{``    ``// using formula to find the``    ``// Nth term t(n) = a(1) + (n-1)*d``    ``return` `(a + (N - 1) * d);``    ` `}` `// Driver code``int` `main()``{``    ``// starting number``    ``int` `a = 2;``    ` `    ``// Common difference``    ``int` `d = 1;``    ` `    ``// N th term to be find``    ``int` `N = 5;``    ` `    ``// Display the output``    ``cout << ``"The "``<< N``         ``<<``"th term of the series is : "``         ``<< Nth_of_AP(a,d,N);` `    ``return` `0;``}`

## Java

 `// Java program to find nth term``// of Arithmetic progression``import` `java.io.*;``import` `java.lang.*;` `class` `GFG``{``    ``public` `static` `int` `Nth_of_AP(``int` `a,``                                ``int` `d,``                                ``int` `N)``    ``{``        ``// using formula to find the Nth``        ``// term t(n) = a(1) + (n-1)*d``        ``return` `( a + (N - ``1``) * d );``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``// starting number``        ``int` `a = ``2``;``        ` `        ``// Common difference``        ``int` `d = ``1``;``        ` `        ``// N th term to be find``        ``int` `N = ``5``;` `        ``// Display the output``        ``System.out.print(``"The "``+ N +``                         ``"th term of the series is : "` `+``                          ``Nth_of_AP(a, d, N));``    ``}``}`

## Python3

 `# Python 3 Program to``# find nth term of``# Arithmetic progression` `def` `Nth_of_AP(a, d, N) :` `    ``# using formula to find the``    ``# Nth term t(n) = a(1) + (n-1)*d``    ``return` `(a ``+` `(N ``-` `1``) ``*` `d)``     ` ` ` `# Driver code``a ``=` `2`  `# starting number``d ``=` `1`  `# Common difference``N ``=` `5`  `# N th term to be find`` ` `# Display the output``print``( ``"The "``, N ,``"th term of the series is : "``,``       ``Nth_of_AP(a, d, N))`   `# This code is contributed``# by Nikita Tiwari.`

## Javascript

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## C#

 `// C# program to find nth term``// of Arithmetic progression``using` `System;` `class` `GFG``{``    ``public` `static` `int` `Nth_of_AP(``int` `a,``                                ``int` `d,``                                ``int` `N)``    ``{``        ` `        ``// using formula to find the Nth``        ``// term t(n) = a(1) + (n-1)*d``        ``return` `( a + (N - 1) * d );``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``// starting number``        ``int` `a = 2;``        ` `        ``// Common difference``        ``int` `d = 1;``        ` `        ``// N th term to be find``        ``int` `N = 5;` `        ``// Display the output``        ``Console.WriteLine(``"The "``+ N +``                          ``"th term of the series is : "` `+``                           ``Nth_of_AP(a, d, N));``    ``}``}` `// This code is contributed by vt_m.`

## PHP

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Output :

`The 5th term of the series is : 6`

Time Complexity: O(1), the code will run in a constant time.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

Approach 2: Using a loop to iterate over each term in the series until the N-th term is reached.

## C++

 `#include ``using` `namespace` `std;` `int` `main()``{``    ``int` `a = 2;``    ``int` `d = 1;``    ``int` `n = 5;``    ` `    ``int` `nthTerm = a;``    ``for` `(``int` `i = 1; i < n; i++)``    ``{``        ``nthTerm += d;``    ``}``    ``cout << ``"The "` `<< n << ``"th term of the series is: "` `<< nthTerm << endl;``    ``return` `0;``}`

## Java

 `import` `java.util.*;` `public` `class` `Main {``    ``public` `static` `void` `main(String[] args) {``        ``int` `a = ``2``;``        ``int` `d = ``1``;``        ``int` `n = ``5``;` `        ``int` `nthTerm = a;``        ``for` `(``int` `i = ``1``; i < n; i++) {``            ``nthTerm += d;``        ``}``        ``System.out.println(``"The "` `+ n + ``"th term of the series is: "` `+ nthTerm);``    ``}``}`

## Python3

 `a ``=` `2``d ``=` `1``n ``=` `5` `nthTerm ``=` `a``for` `i ``in` `range``(``1``, n):``    ``nthTerm ``+``=` `d` `print``(``"The"``, n, ``"th term of the series is:"``, nthTerm)` `# This code is contributed by shivhack999`

## Javascript

 `let a = 2;``let d = 1;``let n = 5;` `let nthTerm = a;``for` `(let i = 1; i < n; i++) {``    ``nthTerm += d;``}``console.log(``"The "` `+ n + ``"th term of the series is: "` `+ nthTerm);`

## C#

 `using` `System;` `public` `class` `MainClass``{``    ``public` `static` `void` `Main(``string``[] args)``    ``{``        ``int` `a = 2;``        ``int` `d = 1;``        ``int` `n = 5;` `        ``int` `nthTerm = a;``        ``for` `(``int` `i = 1; i < n; i++)``        ``{``            ``nthTerm += d;``        ``}``        ``Console.WriteLine(``"The "` `+ n + ``"th term of the series is: "` `+ nthTerm);``    ``}``}`

Output

`The 5th term of the series is: 6`

Time complexity:- O(N), Where N is the term to be found

Space complexity :- O(1)