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Find nth term of the series 5 2 13 41
  • Last Updated : 20 Apr, 2021

Given a number N, the task is to find the nth term of the series 
 

5, 2, 19, 13, 41, 31, 71, 57….

 
It is given that value of n can range between 1 and 10000. 
Examples: 
 

Input: N = 4
Output:13

Input: N = 15
Output:272

Approach: The problem looks very hard but approach is very simple. If the value of n is given as an odd number, the nth term will be ( ( n + 1 ) ^ 2 ) + n. 
Otherwise, it will be ( ( n – 1 ) ^ 2 ) + n.
 



Implementation:
 

C++




// C++ program to find nth term of
// the series 5 2 13 41
#include<bits/stdc++.h>
using namespace std;
 
// function to calculate nth term of the series
int nthTermOfTheSeries(int n)
{
    // to store the nth term of series
    int nthTerm;
 
    // if n is even number
    if (n % 2 == 0)
        nthTerm = pow(n - 1, 2) + n;
 
    // if n is odd number
    else
        nthTerm = pow(n + 1, 2) + n;
 
    // return nth term
    return nthTerm;
}
 
// Driver code
int main()
{
    int n;
 
    n = 8;
    cout << nthTermOfTheSeries(n) << endl;
 
    n = 12;
    cout << nthTermOfTheSeries(n) << endl;
 
    n = 102;
    cout << nthTermOfTheSeries(n) << endl;
 
    n = 999;
    cout << nthTermOfTheSeries(n) << endl;
 
    n = 9999;
    cout << nthTermOfTheSeries(n) << endl;
 
    return 0;
}
 
// This code is contributed
// by Akanksha Rai

C




// C program to find nth term of
// the series 5 2 13 41
#include <math.h>
#include <stdio.h>
 
// function to calculate nth term of the series
int nthTermOfTheSeries(int n)
{
    // to store the nth term of series
    int nthTerm;
 
    // if n is even number
    if (n % 2 == 0)
        nthTerm = pow(n - 1, 2) + n;
 
    // if n is odd number
    else
        nthTerm = pow(n + 1, 2) + n;
 
    // return nth term
    return nthTerm;
}
 
// Driver code
int main()
{
    int n;
 
    n = 8;
 
    printf("%d\n", nthTermOfTheSeries(n));
 
    n = 12;
    printf("%d\n", nthTermOfTheSeries(n));
 
    n = 102;
    printf("%d\n", nthTermOfTheSeries(n));
 
    n = 999;
    printf("%d\n", nthTermOfTheSeries(n));
 
    n = 9999;
    printf("%d\n", nthTermOfTheSeries(n));
 
    return 0;
}

Java




// Java program to find nth term of the series 5 2 13 41
 
import java.lang.Math;
class GFG
{
// function to calculate nth term of the series
static long  nthTermOfTheSeries(int n)
{
    // to store the nth term of series
    long nthTerm;
 
    // if n is even number
    if (n % 2 == 0)
        nthTerm = (long)Math.pow(n - 1, 2) + n;
 
    // if n is odd number
    else
        nthTerm = (long)Math.pow(n + 1, 2) + n;
 
    // return nth term
    return nthTerm;
}
 
// Driver code
public static void main(String[] args)
{
    int n;
 
    n = 8;
 
    System.out.println( nthTermOfTheSeries(n));
 
    n = 12;
    System.out.println( nthTermOfTheSeries(n));
 
    n = 102;
    System.out.println( nthTermOfTheSeries(n));
 
    n = 999;
    System.out.println( nthTermOfTheSeries(n));
     
    n = 9999;
    System.out.println( nthTermOfTheSeries(n));
//This code is contributed by  29AjayKumar
 
}
}

Python3




# Python3 program to find nth term
# of the series 5 2 13 41
from math import pow
 
# function to calculate nth term
# of the series
def nthTermOfTheSeries(n):
     
    # to store the nth term of series
    # if n is even number
    if (n % 2 == 0):
        nthTerm = pow(n - 1, 2) + n
 
    # if n is odd number
    else:
        nthTerm = pow(n + 1, 2) + n
 
    # return nth term
    return nthTerm
 
# Driver code
if __name__ == '__main__':
     
    n = 8
    print(int(nthTermOfTheSeries(n)))
 
    n = 12
    print(int(nthTermOfTheSeries(n)))
 
    n = 102
    print(int(nthTermOfTheSeries(n)))
 
    n = 999
    print(int(nthTermOfTheSeries(n)))
 
    n = 9999
    print(int(nthTermOfTheSeries(n)))
 
# This code is contributed by
# Shashank_Sharma

C#




// C# program to find nth term
// of the series 5 2 13 41
using System;
 
class GFG
{
    // function to calculate
    // nth term of the series
    static long nthTermOfTheSeries(int n)
    {
        // to store the nth term of series
        long nthTerm;
     
        // if n is even number
        if (n % 2 == 0)
            nthTerm = (long)Math.Pow(n - 1, 2) + n;
     
        // if n is odd number
        else
            nthTerm = (long)Math.Pow(n + 1, 2) + n;
     
        // return nth term
        return nthTerm;
    }
     
    // Driver code
    public static void Main()
    {
        int n;
     
        n = 8;
        Console.WriteLine(nthTermOfTheSeries(n));
     
        n = 12;
        Console.WriteLine( nthTermOfTheSeries(n));
     
        n = 102;
        Console.WriteLine( nthTermOfTheSeries(n));
     
        n = 999;
        Console.WriteLine( nthTermOfTheSeries(n));
         
        n = 9999;
        Console.WriteLine( nthTermOfTheSeries(n));
    }
}
 
// This code is contributed by Ryuga

PHP




<?php
// Php program to find nth term of
// the series 5 2 13 41
 
// function to calculate nth term
// of the series
function nthTermOfTheSeries($n)
{
 
    // if n is even number
    if ($n % 2 == 0)
        $nthTerm = pow($n - 1, 2) + $n;
 
    // if n is odd number
    else
        $nthTerm = pow($n + 1, 2) + $n;
 
    // return nth term
    return $nthTerm;
}
 
// Driver code
$n = 8;
echo nthTermOfTheSeries($n) . "\n";
 
$n = 12;
echo nthTermOfTheSeries($n) . "\n";
 
$n = 102;
echo nthTermOfTheSeries($n) . "\n";
 
$n = 999;
echo nthTermOfTheSeries($n) . "\n";
 
$n = 9999;
echo nthTermOfTheSeries($n) . "\n";
 
// This code is contributed by ita_c
?>

Javascript




<script>
// Javascript program to find nth term of
// the series 5 2 13 41
 
// function to calculate nth term of the series
function nthTermOfTheSeries(n)
{
    // to store the nth term of series
    let nthTerm;
 
    // if n is even number
    if (n % 2 == 0)
        nthTerm = Math.pow(n - 1, 2) + n;
 
    // if n is odd number
    else
        nthTerm = Math.pow(n + 1, 2) + n;
 
    // return nth term
    return nthTerm;
}
 
// Driver code
let n;
 
n = 8;
document.write(nthTermOfTheSeries(n) + "<br>");
 
n = 12;
document.write(nthTermOfTheSeries(n) + "<br>");
 
n = 102;
document.write(nthTermOfTheSeries(n) + "<br>");
 
n = 999;
document.write(nthTermOfTheSeries(n) + "<br>");
 
n = 9999;
document.write(nthTermOfTheSeries(n) + "<br>");
 
// This code is contributed by rishavmahato348.
</script>
Output: 
57
133
10303
1000999
100009999

 

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