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

Given first term (a), common ratio (r), and an integer N of the Geometric Progression series, the task is to find the 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: 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 N^th term in the Geometric Progression series we use the simple formula as shown below as follows:

T_{N = 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)

Approach 2(Using Loop): To solve the problem follow the below idea:

Initialize a variable NthTerm to hold the Nth term of the geometric progression series, and set it equal to the first term of the series.
Use a for loop to iterate over the first N-1 terms of the series, multiplying each term by the common ratio to get the next term.
Print out the calculated Nth term of the series.

Below is the implementation of the above approach:

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)
    {
        int NthTerm = a;
        for (int i = 1; i < N; i++) {
            NthTerm *= r;
        }
        return NthTerm;
    }
 
    // 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));
    }
}