Program to find Nth term of series 7, 21, 49, 91, 147, 217, ……

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++

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// CPP 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;
}

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Java

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// 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));
  
}
  
}

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Python3

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# Python 3 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))

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C#

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// 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

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PHP

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<?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
?> 

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Output:

91

Time Complexity: O(1)



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