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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