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++

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// 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; 

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Java

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// 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)); 
    

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Python3

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# 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 

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C#

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// 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 

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PHP

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<?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. 
?> 

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Output :

The 5th term of the series is : 162


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