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++ 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 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 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# 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 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 ?> |
<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> |
91
Time Complexity: O(1)
Auxiliary Space: O(1)