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Find Nth term of the series 5, 13, 25, 41, 61…

  • Difficulty Level : Easy
  • Last Updated : 15 Mar, 2021

Given a number N. The task is to write a program to find the Nth term in the below series: 
 

5, 13, 25, 41, 61...

Examples: 
 

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Input : 3
Output : 25
For N = 3
Nth term = 3*3 + (3+1)*(3+1)
         = 25
Input : 5
Output : 61

 

On observing carefully, the Nth term of the given series can be generalised as: 
 



Nth term = N2 + (N+1)2

Below is the implementation of the above approach:
 

C++




// CPP program to find N-th term of the series:
// 5, 13, 25, 41, 61...
#include <iostream>
using namespace std;
 
// calculate Nth term of series
int nthTerm(int N)
{
    return N * N + (N + 1) * (N + 1);
}
 
// Driver Function
int main()
{
    int N = 3;
 
    cout << nthTerm(N);
 
    return 0;
}

Java




// Java program to calculate Nth term of
// the series: 5, 13, 25, 41, 61...
 
import java.io.*;
 
class Nth {
    public static int nthTerm(int N)
    {
        // By using above formula
        return N * N + (N + 1) * (N + 1);
    }
     
    public static void main(String[] args)
    {
        int N = 3; // Nth term is 25
         
        // call and print Nth term
        System.out.println(nthTerm(N));
    }   
}

Python 3




# Python 3 program to find
# N-th term of the series:
# 5, 13, 25, 41, 61...
 
# Function to calculate
# Nth term of series
def nthTerm(N) :
    return N * N + (N + 1) * (N + 1)
 
# Driver Code
if __name__ == "__main__" :
 
    N = 3
 
    # function calling
    print(nthTerm(N))
 
# This code is contributed
# by ANKITRAI1

C#




// C# program to calculate Nth term of
// the series: 5, 13, 25, 41, 61...
using System;
 
class GFG
{
public static int nthTerm(int N)
{
    // By using above formula
    return N * N + (N + 1) * (N + 1);
}
 
// Driver Code
public static void Main()
{
    int N = 3; // Nth term is 25
     
    // call and print Nth term
    Console.Write(nthTerm(N));
}
}
 
// This code is contributed
// by ChitraNayal

PHP




<?php
// PHP program to find N-th
// term of the series:
// 5, 13, 25, 41, 61...
 
// calculate Nth term of series
function nthTerm($N)
{
    return $N * $N + ($N + 1) *
                     ($N + 1);
}
 
// Driver Code
$N = 3;
 
echo nthTerm($N);
 
// This code is contributed
// by ChitraNayal
?>

Javascript




<script>
 
// JavaScript program to find N-th term of the series:
// 5, 13, 25, 41, 61...
 
// calculate Nth term of series
function nthTerm( N)
{
    return N * N + (N + 1) * (N + 1);
}
// Driver Function
 
    let N = 3;
    document.write(nthTerm(N));
     
// This code contributed by Rajput-Ji
 
</script>
Output: 
25

 

Time Complexity: O(1)
 




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