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Program to find Nth term of series 7, 21, 49, 91, 147, 217, ……
  • Last Updated : 31 Mar, 2021

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

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

Examples:  

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

Input: N = 10
Output: 636

Given series is:  

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



On taking 7 commons from all of the terms, we get:  

7 * (1, 3, 7, 13, 21, 31,…..), ….. 
 

Now, for the inner-series: 1,3,7,13,21,… 
On careful observation we can express the terms of above series as: 
1 = (12) – (1-1) 
3 = (22) – (2-1) 
7 = (32) – (3-1) 
13 = (42) – (4-1) 
21 = (52) – (5-1) 



n-th term = (n2) – (n-1)
Therefore, the n-th term of the actual series will be: 

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

Below is the implementation of the above approach:  

C++




// 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




// 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




# 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#




// 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
// 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
?>

Javascript




<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>
Output: 
91

 

Time Complexity: O(1)
 

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