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Program to find Nth term of the series 3 , 5 , 21 , 51 , 95 , …
  • Difficulty Level : Medium
  • Last Updated : 23 Oct, 2018

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

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
?>


Output:

51

Time Complexity: O(1)

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