Programa para hallar el término N de la serie 7, 21, 49, 91, 147, 217, ……

Dado un número N. La tarea es escribir un programa para encontrar el N-ésimo término de la siguiente serie:

7, 21, 49, 91, 147, 217, 301, 399, …(Términos N)

Ejemplos :  

Input: N = 4
Output: 91
For N = 4
4th Term = ( 7 * 4 * 4 - 7 * 4 + 7) 
         = 91

Input: N = 10
Output: 636

serie dada es:  

7, 21, 49, 91, 147, 217, 301, 399 , …..

Al tomar 7 comunes de todos los términos, obtenemos:  

7 * (1, 3, 7, 13, 21, 31,…..) , ….. 
 

Ahora, para la serie interna: 1,3,7,13,21,… Observando 
detenidamente, podemos expresar los términos de la serie anterior como: 
1 = (1 ² ) – (1-1) 
3 = (2 ² ) – (2-1) 
7 = (3 ² ) – (3-1) 
13 = (4 ² ) – (4-1) 
21 = (5 ² ) – (5-1) 
. 
. 
. 
n-ésimo término = (n ² ) – (n-1)
Por lo tanto, el n-ésimo término de la serie real será: 

N-th term = 7 * ((n2) - (n-1))
          = 7 * (n2 - n + 1)

A continuación se muestra la implementación del enfoque anterior:  

// C++ program to find the N-th term of the series:
// 7, 21, 49, 91, 146, 217, 301, 399, ...
#include <iostream>
#include <math.h>
using namespace std;
 
// calculate Nth term of series
int nthTerm(int n)
{
    return 7 * pow(n, 2) - 7 * n + 7;
}
 
// Driver code
int main()
{
    int N = 4;
 
    cout << nthTerm(N);
 
    return 0;
}

// Java program to find the N-th term of the series:
// 7, 21, 49, 91, 146, 217, 301, 399, ...
 
// calculate Nth term of series
import java.util.*;
 
class solution
{
 
//Function to find the nth term of the series
static int nthTerm(int n)
{
    return 7 * (int)Math.pow(n, 2) - 7 * n + 7;
}
 
// Driver code
public static void main(String arr[])
{
    int N = 4;
 
    System.out.println(nthTerm(N));
 
}
 
}

# Python3 program to find the N-th term of the series:
# 7, 21, 49, 91, 146, 217, 301, 399, ...
 
 
# calculate Nth term of series
def nthTerm( n):
 
    return 7 * pow(n, 2) - 7 * n + 7
 
 
# Driver code
N = 4
 
print(nthTerm(N))

// C# program to find the
// N-th term of the series:
// 7, 21, 49, 91, 146, 217, 301, 399, ...
using System;
 
// calculate Nth term of series
class GFG
{
 
// Function to find the Nth
// term of the series
static int nthTerm(int n)
{
    return 7 * (int)Math.Pow(n, 2) - 7 * n + 7;
}
 
// Driver code
public static void Main()
{
    int N = 4;
 
    Console.WriteLine(nthTerm(N));
}
}
 
// This code is contributed
// by Akanksha Rai

<?php
// PHP program to find the
// N-th term of the series:
// 7, 21, 49, 91, 146, 217, 301, 399, ...
function Sum_upto_nth_Term($n)
{
    $r = 7 * pow($n, 2) - 7 * $n + 7;
    echo $r;
}
 
// Driver code
$N = 4;
Sum_upto_nth_Term($N);
 
// This code is contributed
// by Sanjit_Prasad
?>

<script>
 
// Javascript program to find the N-th term
// of the series:
// 7, 21, 49, 91, 146, 217, 301, 399, ...
 
// Calculate Nth term of series
function nthTerm(n)
{
    return 7 * Math.pow(n, 2) - 7 * n + 7;
}
 
// Driver code
let N = 4;
 
document.write(nthTerm(N));
 
// This code is contributed by Surbhi Tyagi.
 
</script>

91

Complejidad de tiempo: O(1)

Espacio Auxiliar: O(1)