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Program for N-th term of Geometric Progression series

  • Difficulty Level : Easy
  • Last Updated : 25 Feb, 2021

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: 
 

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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++




// 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;
}

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;
 
        // Display the output
        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
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

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;
 
        // 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

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;
     
// Display the output
echo("The " . $N . "th term of the series is : "
                    . Nth_of_GP($a, $r, $N));
 
// This code is contributed by Ajit.
?>

Javascript




<script>
 
// 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
 
</script>

Output : 
 

The 5th term of the series is : 162

 




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