# 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 N^{th} 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 :

t_{1}= a_{1}

t_{2}= a_{1}* r^{(2-1)}

t_{3}= a_{1}* r^{(3-1)}

t_{4}= a_{1}* r^{(4-1)}

.

.

.

.

t_{N}= a_{1}* r^{(N-1)}

To find the N^{th} term in the Geometric Progression series we use the simple formula .

T_{N = a1 * r(N-1)}

## C++

`// CPP Program to find nth term of ` `// geometric progression ` `#include <bits/stdc++.h>` ` ` `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

`<?php ` `// PHP Program to find nth term of ` `// geometric progression ` `function` `Nth_of_GP(` `$a` `, ` `$r` `, ` `$N` `) ` `{ ` ` ` `// using formula to find ` ` ` `// the Nth term TN = a1 * r(N-1) ` ` ` `return` `( ` `$a` `* (int)(pow(` `$r` `, ` `$N` `- 1)) ); ` ` ` `} ` `// Driver code ` `// starting number ` `$a` `= 2; ` `// Common ratio ` `$r` `= 3; ` `// N th term to be find ` `$N` `= 5; ` ` ` `// Display the output ` `echo` `(` `"The "` `. ` `$N` `. ` `"th term of the series is : "` ` ` `. Nth_of_GP(` `$a` `, ` `$r` `, ` `$N` `)); ` `// This code is contributed by Ajit. ` `?> ` |

## Javascript

`<script>` `// JavaScript Program to find nth term of ` `// geometric progression ` ` ` `function` `Nth_of_GP(a, r, N) ` `{ ` ` ` `// using formula to find ` ` ` `// the Nth term ` ` ` `// TN = a1 * r(N-1) ` ` ` `return` `( a * Math.floor(Math.pow(r, N - 1)) ); ` ` ` `} ` ` ` `// Driver code ` ` ` ` ` `// starting number ` ` ` `let a = 2; ` ` ` ` ` `// Common ratio ` ` ` `let r = 3; ` ` ` ` ` `// N th term to be find ` ` ` `let N = 5; ` ` ` ` ` `// Display the output ` ` ` `document.write(` `"The "` `+ N +` `"th term of the series is : "` ` ` `+ Nth_of_GP(a, r, N)); ` ` ` ` ` `// This code is contributed by Surbhi Tyagi` `</script>` |

**Output :**

The 5th term of the series is : 162

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