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++

// 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;
}

Java

// 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..

Python 3

# 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

C#

// 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

PHP

<?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
?>

Javascript

<script>

// Javascript 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
    let n = 3;

    // find the Sn
    document.write("Sum = " + calculateSum(n));


// This code is contributed by Mayank Tyagi

</script>

Output:

Sum = 40

Time Complexity: O(1), the code will run in a constant time.
Auxiliary Space: O(1), no extra space is required, so it is a constant.