Sum of the first N terms of the series 5,12, 23, 38….

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

Sn = 5 + 12 + 23 + 38 + … upto n terms

Examples:



Input: N = 2
Output: 17
5 + 12
= 17

Input: N = 4 
Output: 80
5 + 12 + 23 + 38
= 78

Approach: Let, the nth term be denoted by tn.
This problem can easily with the help of a general formula for these type of series,

The series given above is a quadratic series. They are special because the difference of consecutive terms of this series will be in arithmetic progression.
There general formula is given by:

General Formula = a*(n^2) + b*n + c

Now, by putting first 3 terms of series in general formula we can get values of a, b and c.

Sn = 5 + 12 + 30 + 68 + ......
tn = 2 * (n^2) + n + 2
Sn = 2 * (n * (n+1) * (2 * n+1)/6) + n * (n+1)/2 + 2 * (n)

Below is the implementation of above approach:

C++

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// C++ program to find sum of first n terms
#include <bits/stdc++.h>
using namespace std;
  
// Function to calculate the sum
int calculateSum(int n)
{
  
    return 2 * (n * (n + 1) * (2 * n + 1) / 6) 
               + n * (n + 1) / 2 + 2 * (n);
}
  
// Driver code
int main()
{
    // number of terms to be included in sum
    int n = 3;
  
    // find the Sn
    cout << "Sum = " << calculateSum(n);
  
    return 0;
}

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Java

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// Java program to find sum of first n terms
  
import java.io.*;
  
class GFG {
  
// Function to calculate the sum
 static int calculateSum(int n)
{
  
    return 2 * (n * (n + 1) * (2 * n + 1) / 6
            + n * (n + 1) / 2 + 2 * (n);
}
  
// Driver code
  
    public static void main (String[] args) {
        // number of terms to be included in sum
    int n = 3;
  
    // find the Sn
    System.out.print( "Sum = " + calculateSum(n));
    }
}
// This code is contributed 
// by  anuj_67..

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Python 3

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# Python program to find 
# sum of first n terms
  
# Function to calculate the sum 
def calculateSum(n) :
  
    return (2 * (n * (n + 1) * 
           (2 * n + 1) // 6) + n *
           (n + 1) // 2 + 2 * (n))
          
# Driver code     
if __name__ == "__main__" :
  
    # number of terms to be
    # included in sum 
    n = 3
  
    # find the Sn 
    print("Sum =",calculateSum(n)) 
  
# This code is contributed by ANKITRAI1

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C#

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// C# program to find sum 
// of first n terms
using System;
  
class GFG
{
  
// Function to calculate the sum
static int calculateSum(int n)
{
  
    return 2 * (n * (n + 1) * (2 * n + 1) / 6) +
                n * (n + 1) / 2 + 2 * (n);
}
  
// Driver code
public static void Main () 
{
    // number of terms to be
    // included in sum
    int n = 3;
      
    // find the Sn
    Console.WriteLine("Sum = " + calculateSum(n));
}
}
  
// This code is contributed 
// by Shashank

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PHP

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<?php 
// PHP program to find sum 
// of first n terms
  
// Function to calculate the sum
function calculateSum($n)
{
  
    return 2 * ($n * ($n + 1) * 
            (2 * $n + 1) / 6) + 
                $n * ($n + 1) / 
                2 + 2 * ($n);
}
  
// Driver code
  
// number of terms to 
// be included in sum
$n = 3;
  
// find the Sn
echo "Sum = " . calculateSum($n);
  
// This code is contributed
// by ChitraNayal
?>

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Output:

Sum = 40


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