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Program to find Nth term of given Geometric Progression (GP) series

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  • Difficulty Level : Easy
  • Last Updated : 14 Sep, 2022
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Given first term (a), common ratio (r), and an integer N of the Geometric Progression series, the task is to find the 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: To solve the problem follow the below idea:

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 as shown below as follows: 

TN = a1 * r(N-1)

Below is the implementation of the above approach:

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;
 
    // Function call
    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;
 
        // Function call
        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
if __name__ == "__main__":
  a = 2  # Starting number
  r = 3  # Common ratio
  N = 5  # N th term to be find
 
  # Function call
  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;
 
        // Function call
        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;
     
// Function call
echo("The " . $N . "th term of the series is : "
                    . Nth_of_GP($a, $r, $N));
 
// This code is contributed by Ajit.
?>


Javascript




// 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


Output

The 5th term of the series is : 162

Time complexity: O(log N) because using the inbuilt pow function
Auxiliary Space: O(1)


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