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));
    }
}

Output

The 5th term of the series is : 162

Time complexity: O(log N) 
Auxiliary Space: O(1)