# 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