Find sum of the series ?3 + ?12 +……… upto N terms

Given a number n, the task is to find the sum of first n terms of this series. Below is the series: 

Examples:

Input: n = 10
Output: 95.2628

Input: n = 5
Output: 25.9808

This series can be seen as- 

Below is the required implementation:

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
#define ll long long int
using namespace std;

// Function to find the sum
double findSum(ll n)
{

    // Apply AP formula
    return sqrt(3) * (n * (n + 1) / 2);
}
// Driver code
int main()
{
    // number of terms
    ll n = 10;

    cout << findSum(n) << endl;
    return 0;
}

Java

// Java implementation of
// above approach
import java.io.*;

class GFG
{

// Function to find the sum
static double findSum(long n)
{
    // Apply AP formula
    return Math.sqrt(3) * (n *
                    (n + 1) / 2);
}
// Driver code
public static void main (String[] args)
{
    // number of terms
    long n = 10;

    System.out.println( findSum(n));
}
}

// This code is contributed
// by inder_verma..

Python3

# Python3 implementation of above approach

#Function to find the sum
import math
def findSum(n):
    # Apply AP formula
    return math.sqrt(3) * (n * (n + 1) / 2)

# Driver code
# number of terms
if __name__=='__main__':
    n = 10
    print(findSum(n))

# This code is contributed by sahilshelangia

C#

// C# implementation of
// above approach
using System;

class GFG
{

// Function to find the sum
static double findSum(long n)
{
    // Apply AP formula
    return Math.Sqrt(3) * (n *
                    (n + 1) / 2);
}
// Driver code
public static void Main ()
{
    // number of terms
    long n = 10;

    Console.WriteLine( findSum(n));
}
}

// This code is contributed
// by inder_verma..

PHP

<?php
// PHP implementation of above approach

// Function to find the sum
function findSum($n)
{

    // Apply AP formula
    return sqrt(3) * ($n * ($n + 1) / 2);
}

// Driver code

// number of terms
$n = 10;

echo findSum($n);

// This code is contributed
// by inder_verma
?>

Javascript

<script>
// Javascript implementation of
// above approach

    // Function to find the sum
    function findSum( n)
    {

        // Apply AP formula
        return Math.sqrt(3) * (n * (n + 1) / 2);
    }

    // Driver code

    // number of terms
    let n = 10;

    document.write(findSum(n).toFixed(4));

// This code is contributed by 29AjayKumar
</script>

Output:

95.2628

Time complexity: O(1) since performing constant operations

Auxiliary Space: O(1) for constant space for variables