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  


// 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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