Program to print the Sum of series -1 + 2 + 11 + 26 + 47 +…..

Difficulty Level : Hard
Last Updated : 22 Mar, 2021

Given a number N, the task is to find the sum of first N number of series:

-1, 2, 11, 26, 47, 74, …..

Examples:

Input: N = 3
Output: 12
Explanation:
Sum = (N * (N + 1) * (2 * N - 5) + 4 * N) / 2
    = (3 * (3 + 1) * (2 * 3 - 5) + 4 * 3) / 2
    = 12

Input: N = 9
Output: 603

Approach:
The Nth term of the given series can be generalised as:
Nth term of the series $T_n =3 * n * n - 6 * n + 2$
$S_n=3\sum_{i=1}^n N^2 - 6\sum_{i=1}^n N+ 2 \sum_{i=1}^n 1\\\\ S_n=3*\frac{n(n+1)(2n+1)}{6}-6*\frac{n(n+1)}{2} +2n\\\\ S_n=\frac{n(n+1)(2n-5)+4n}{2}$
Below is the implementation of the above approach:

C++

// CPP program to find SUM
// upto N-th term of the series:
// -1, 2, 11, 26, 47, 74, .....
 
#include <iostream>
using namespace std;
 
// calculate Nth term of series
int findSum(int N)
{
    return (N * (N + 1) * (2 * N - 5) + 4 * N) / 2;
}
 
// Driver Function
int main()
{
 
    // Get the value of N
    int N = 3;
 
    // 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:
// -1, 2, 11, 26, 47, 74, .....
import java.util.*;
 
class solution
{
 static int findSum(int N)
{
 return (N * (N + 1) * (2 * N - 5) + 4 * N) / 2;
}
 
//driver function
public static void main(String arr[])
{
  // Get the value of N
    int N = 3;
 
 // Get the sum of the series
   System.out.println(findSum(N));
 
}
}
//THis code is contributed by
//Surendra_Gangwar

Python3

# Python3 program to find sum
# upto N-th term of the series:
# -1, 2, 11, 26, 47, 74, .....
 
# calculate Nth term of series
def findSum(N):
     
    return ((N * (N + 1) *
           (2 * N - 5) + 4 * N) / 2)
     
#Driver Function
if __name__=='__main__':
     
    #Get the value of N
    N = 3
 
    #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:
// -1, 2, 11, 26, 47, 74, .....
using System;
 
class GFG
{
static int findSum(int N)
{
    return (N * (N + 1) *
           (2 * N - 5) + 4 * N) / 2;
}
 
// Driver Code
static public void Main ()
{
    // Get the value of N
    int N = 3;
     
    // 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:
// -1, 2, 11, 26, 47, 74, .....
 
// calculate Nth term of series
function findSum($N)
{
    return ($N * ($N + 1) *
             (2 * $N - 5) + 4 * $N) / 2;
}
 
// Driver Code
 
// Get the value of N
$N = 3;
 
// Get the sum of the series
echo findSum($N) . "\n";
 
// This code is contributed
// by Akanksha Rai(Abby_akku)
?>

Javascript

<script>
// javascript program to find SUM
// upto N-th term of the series:
// -1, 2, 11, 26, 47, 74, .....
 
 
 
function findSum(N)
{
    return (N * (N + 1) * (2 * N - 5) + 4 * N) / 2;
}
 
//driver function
 
  // Get the value of N
    var N = 3;
 
 // Get the sum of the series
   document.write(findSum(N));
 
 
// This code is contributed by 29AjayKumar
 
</script>

Output:

Time Complexity: O(1)

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