Programa para el N-ésimo término de la serie Progresión Geométrica

Dado el primer término (a), la razón común (r) y un número entero N de la serie de progresión geométrica, la tarea es encontrar el término N ^de la serie.
Ejemplos: 
 

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

Acercarse: 
 

Sabemos que la serie de Progresión Geométrica es como = 2, 4, 8, 16, 32…. … 
En esta serie 2 es el término declarante de la serie. 
Razón común = 4 / 2 = 2 (razón común en la serie). 
entonces podemos escribir la serie como:
t ₁ = a ₁ 
t ₂ = a ₁ * r ^(2-1) 
t ₃ = a ₁ * r ^(3-1) 
t ₄ = a ₁ * r ^(4-1) 
. 
. 
. 
. 
t _norte = un ₁ * r ^(n-1)

Para encontrar el N ^-ésimo término en la serie de Progresión Geométrica usamos la fórmula simple. 
 

TN = a1 * r(N-1)

// 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 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 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# 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 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.
?>

<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>

Producción : 
 

The 5th term of the series is : 162