Given a number N, the task is to find the Nth term of the below series:
23 + 45 + 75 + 113 + 159 +…… upto N terms
Examples:
Input: N = 4 Output: 256 Explanation: Nth term = (2 * N * (N + 1) * (4 * N + 17) + 54 * N) / 6 = (2 * 4 * (4 + 1) * (4 * 4 + 17) + 54 * 4) / 6 = 256 Input: N = 10 Output: 2180
Approach:
The Nth term of the given series can be generalized as:
Sum of first n terms of this series:
Therefore, Sum of first n terms of this series:
Below is the implementation of the above approach:
C++
// CPP program to find sum // upto N-th term of the series: // 23, 45, 75, 113... #include <iostream> using namespace std;
// calculate Nth term of series int findSum( int N)
{ return (2 * N * (N + 1) * (4 * N + 17) + 54 * N) / 6;
} // Driver Function int main()
{ // Get the value of N
int N = 4;
// Get the sum of the series
cout << findSum(N) << endl;
return 0;
} |
Java
// Java program to find sum // upto N-th term of the series: // 23, 45, 75, 113... import java.util.*;
class solution
{ static int findSum( int N)
{ //return the final sum
return ( 2 * N * (N + 1 ) * ( 4 * N + 17 ) + 54 * N) / 6 ;
} //Driver program public static void main(String arr[])
{ // Get the value of N int N = 4 ;
// Get the sum of the series System.out.println(findSum(N));
} } |
Python3
# Python3 program to find sum # upto N-th term of the series: # 23, 45, 75, 113... # calculate Nth term of series def findSum(N):
return ( 2 * N * (N + 1 ) * ( 4 * N + 17 ) + 54 * N) / 6
#Driver Function if __name__ = = '__main__' :
#Get the value of N N = 4
#Get the sum of the series print (findSum(N))
#this code is contributed by Shashank_Sharma |
C#
// C# program to find sum // upto N-th term of the series: // 23, 45, 75, 113... using System;
class GFG
{ static int findSum( int N)
{ //return the final sum
return (2 * N * (N + 1) *
(4 * N + 17) + 54 * N) / 6;
} // Driver Code static void Main()
{ // Get the value of N
int N = 4;
// Get the sum of the series
Console.Write(findSum(N));
} } // This code is contributed by Raj |
PHP
<?php // PHP program to find sum // upto N-th term of the series: // 23, 45, 75, 113... // calculate Nth term of series function findSum( $N )
{ return (2 * $N * ( $N + 1) *
(4 * $N + 17) + 54 * $N ) / 6;
} // Driver Code // Get the value of N $N = 4;
// Get the sum of the series echo findSum( $N );
// This code is contributed // by anuj_67 ?> |
Javascript
<script> // javascript program to find sum // upto N-th term of the series: // 23, 45, 75, 113... // calculate Nth term of series function findSum( N)
{ return (2 * N * (N + 1) * (4 * N + 17) + 54 * N) / 6;
} // Driver Function // Get the value of N
let N = 4;
// Get the sum of the series
document.write(findSum(N));
// This code is contributed by Rajput-Ji </script> |
Output:
256
Time Complexity: O(1)
Auxiliary Space: O(1) since using constant variables