Find the sum of series 3, 7, 13, 21, 31….

Given a number N. The task is to find the sum of below series upto n^th term.

3, 7, 13, 21, 31, ….

Examples: 

Input : N = 3
Output : 23

Input : N = 25
Output : 5875

Approach:

Subtracting the above two equations, we have: 

Below is the implementation of the above approach:

C++

// C++ Program to find the sum of given series

#include <iostream>
#include <math.h>

using namespace std;

// Function to calculate sum
int findSum(int n)
{
    // Return sum
    return (n * (pow(n, 2) + 3 * n + 5)) / 3;
}

// Driver code
int main()
{
    int n = 25;

    cout << findSum(n);

    return 0;
}

Java

// Java program to find sum of
// n terms of the given series
import java.util.*;

class GFG
{
static int calculateSum(int n)
{
    // returning the final sum
    return (n * ((int)Math.pow(n, 2) + 3 *
                               n + 5)) / 3;
}

// Driver Code
public static void main(String arr[])
{
    // number of terms to
    // find the sum
    int n = 25;
    System.out.println(calculateSum(n));
}
}

// This code is contributed
// by Surendra_Gangwar

Python 3

# Python program to find the
# sum of given series

# Function to calculate sum
def findSum(n):
    # Return sum
    return (n*(pow(n, 2)+3 * n + 5))/3

# driver code
n = 25

print(int(findSum(n)))

C#

// C# program to find
// sum of n terms of
// the given series
using System;

class GFG
{
static int calculateSum(int n)
{
    // returning the final sum
    return (n * ((int)Math.Pow(n, 2) + 3 *
                               n + 5)) / 3;
}

// Driver Code
public static void Main()
{
    // number of terms to
    // find the sum
    int n = 25;
    Console.WriteLine(calculateSum(n));
}
}

// This code is contributed
// by inder_verma.

PHP

<?php
// PHP Program to find the
// sum of given series

// Function to calculate sum
function findSum($n)
{
    // Return sum
    return ($n * (pow($n, 2) +
             3 * $n + 5)) / 3;
}

// Driver code
$n = 25;

echo findSum($n);

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

Javascript

<script>

// javascript program to find sum of
// n terms of the given series


function calculateSum(n)
{
    // returning the final sum
    return (n * (parseInt(Math.pow(n, 2) + 3 *
                               n + 5)) / 3);
}

// Driver Code
// number of terms to
// find the sum
var n = 25;
document.write(calculateSum(n));


// This code contributed by shikhasingrajput

</script>

Output:

5875

Time Complexity : O(1)

Auxiliary Space: O(1)