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


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++

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// 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;
}

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Java














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// 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 



















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Python3














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# 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 



















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C#














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// 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 



















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PHP














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<?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) 


?> 



















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Output:


12





Time Complexity: O(1)


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