# Program for N-th term of Geometric Progression series

Given first term (a), common ratio (r) and a integer N of the Geometric Progression series, the task is to find Nth term of the series.

Examples :

```Input : a = 2 r = 2, N = 4
Output :
The 4th term of the series is : 16

Input : a = 2 r = 3, N = 5
Output :
The 5th term of the series is : 162
```

Approach:

We know the Geometric Progression series is like = 2, 4, 8, 16, 32 …. …
In this series 2 is the stating term of the series .
Common ratio = 4 / 2 = 2 (ratio common in the series).
so we can write the series as :

t1 = a1
t2 = a1 * r(2-1)
t3 = a1 * r(3-1)
t4 = a1 * r(4-1)
.
.
.
.
tN = a1 * r(N-1)

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

```TN = a1 * r(N-1)
```

## C++

 `// CPP Program to find nth term of  ` `// geometric progression  ` `#include ` `  `  `using` `namespace` `std;  ` ` `  `int` `Nth_of_GP(``int` `a, ``int` `r, ``int` `N)  ` `{  ` `    ``// using formula to find  ` `    ``// the Nth term  ` `    ``// TN = a1 * r(N-1)  ` `    ``return``( a * (``int``)(``pow``(r, N - 1)) );  ` `     `  `}  ` ` `  `// Driver code  ` `int` `main()  ` `{  ` `    ``// starting number  ` `    ``int` `a = 2;  ` `     `  `    ``// Common ratio  ` `    ``int` `r = 3;  ` `     `  `    ``// N th term to be find  ` `    ``int` `N = 5;  ` `     `  `    ``// Display the output  ` `    ``cout << ``"The "``<< N <<``"th term of the series is : "` `        ``<< Nth_of_GP(a, r, N);  ` ` `  `    ``return` `0;  ` `}  `

## Java

 `// java program to find nth term  ` `// of geometric progression  ` `import` `java.io.*;  ` `import` `java.lang.*;  ` ` `  `class` `GFG  ` `{  ` `    ``public` `static` `int` `Nth_of_GP(``int` `a,  ` `                                ``int` `r,  ` `                                ``int` `N)  ` `    ``{  ` `        ``// using formula to find the Nth  ` `        ``// term TN = a1 * r(N-1)  ` `        ``return` `( a * (``int``)(Math.pow(r, N - ``1``)) );  ` `    ``}  ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{  ` `        ``// starting number  ` `        ``int` `a = ``2``;  ` `         `  `        ``// Common ratio  ` `        ``int` `r = ``3``;  ` `         `  `        ``// 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_GP(a, r, N));  ` `    ``}  ` `}  `

## Python3

 `# Python3 Program to find nth  ` `# term of geometric progression  ` `import` `math  ` ` `  `def` `Nth_of_GP(a, r, N):  ` ` `  `    ``# Using formula to find the Nth  ` `    ``# term TN = a1 * r(N-1)  ` `    ``return``( a ``*` `(``int``)(math.``pow``(r, N ``-` `1``)) )  ` `     `  `# Driver code  ` `a ``=` `2` `# Starting number  ` `r ``=` `3` `# Common ratio  ` `N ``=` `5` `# N th term to be find  ` `     `  `print``(``"The"``, N, ``"th term of the series is :"``,  ` `                            ``Nth_of_GP(a, r, N))  ` ` `  ` `  `# This code is contributed by Smitha Dinesh Semwal  `

## C#

 `// C# program to find nth term  ` `// of geometric progression  ` `using` `System;  ` ` `  `class` `GFG  ` `{  ` `     `  `    ``public` `static` `int` `Nth_of_GP(``int` `a,  ` `                                ``int` `r,  ` `                                ``int` `N)  ` `    ``{  ` `         `  `        ``// using formula to find the Nth  ` `        ``// term TN = a1 * r(N-1)  ` `        ``return` `( a * (``int``)(Math.Pow(r, N - 1)) );  ` `    ``}  ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `Main()  ` `    ``{  ` `        ``// starting number  ` `        ``int` `a = 2;  ` `         `  `        ``// Common ratio  ` `        ``int` `r = 3;  ` `         `  `        ``// N th term to be find  ` `        ``int` `N = 5;  ` ` `  `        ``// Display the output  ` `        ``Console.Write(``"The "``+ N + ``"th term of the"` `+  ` `            ``" series is : "` `+ Nth_of_GP(a, r, N));  ` `    ``}  ` `}  ` ` `  `// This code is contributed by vt_m  `

## PHP

 `  `

Output :

```The 5th term of the series is : 162
```

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