Skip to content
Related Articles

Related Articles

Improve Article

Program to find Nth term of the series 3 , 5 , 21 , 51 , 95 , …

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

Given a number N, the task is to find the Nth term of this series:
 

3, 5, 21, 51, 95, ….

Examples: 
 

Input: N = 4
Output: 51
Explanation:
Nth term = (7 * pow(N, 2) - 19 * N + 15)
         = (7 * pow(4, 2) - 19 * 4 + 15)
         = 51

Input: N = 10
Output: 525

 

Approach:
The Nth term of the given series can be generalized as: 
 



T_n = 7 * n * n - 14 * n + 15[Tex] [/Tex]

Below is the implementation of the above approach:
 

 

C++




// CPP program to find N-th term of the series:
// 3, 5, 21, 51, 95,...
 
#include <iostream>
#include <math.h>
using namespace std;
 
// calculate Nth term of series
int getNthTerm(long long int N)
{
    // Return Nth term
    return (7 * pow(N, 2) - 19 * N + 15);
}
 
// driver code
int main()
{
    // declaration of number of terms
    long long int N = 4;
 
    // Get the Nth term
    cout << getNthTerm(N);
 
    return 0;
}

Java




// Java program to find N-th term of the series:
// 3, 5, 21, 51, 95,...
import java.util.*;
 
class solution
{
static long getNthTerm(long N)
{
// Return Nth term
    return (7 *(int) Math.pow(N, 2) - 19 * N + 15);
}
 
//Driver program
public static void main(String arr[])
{
// declaration of number of terms
    long N = 4;
 
    // Get the Nth term
     System.out.println(getNthTerm(N));
}
}

Python3




# Python3 program to find N-th term
# of the series:
# 3, 5, 21, 51, 95,...
 
# calculate Nth term of series
def getNthTerm(N):
     
    #Return Nth term
    return (7 * pow(N, 2) - 19 * N + 15)
     
#Driver code
if __name__=='__main__':
     
#declaration of number of terms
    N = 4
 
#Get the Nth term
    print(getNthTerm(N))
 
#this code is contributed by Shashank_Sharma

C#




// C# program to find
// N-th term of the series:
// 3, 5, 21, 51, 95,...
using System;
 
class GFG
{
static long getNthTerm(long N)
{
    // Return Nth term
    return (7 *(int) Math.Pow(N, 2) -
                       19 * N + 15);
}
 
// Driver Code
static public void Main ()
{
 
    // declaration of number
    // of terms
    long N = 4;
 
    // Get the Nth term
    Console.Write(getNthTerm(N));
}
}
 
// This code is contributed by Raj

PHP




<?php
// PHP program to find
// N-th term of the series:
// 3, 5, 21, 51, 95,...
 
// calculate Nth term of series
function getNthTerm($N)
{
    // Return Nth term
    return (7 * pow($N, 2) -
            19 * $N + 15);
}
 
// Driver code
 
// declaration of number
// of terms
$N = 4;
 
// Get the Nth term
echo getNthTerm($N);
 
// This code is contributed
// by anuj_67
?>

Javascript




<script>
 
// JavaScript  program to find N-th term of the series:
// 3, 5, 21, 51, 95,...
 
 
// calculate Nth term of series
function getNthTerm(N)
{
    // Return Nth term
    return (7 * Math.pow(N, 2) - 19 * N + 15);
}
 
// driver code
  // declaration of number of terms
   let N = 4;
   document.write( getNthTerm(N) );
 
// This code contributed by gauravrajput1
 
</script>
Output: 
51

 

Time Complexity: O(1)
 

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.




My Personal Notes arrow_drop_up
Recommended Articles
Page :