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

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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:

$Let $$S=0+3+7+13+21+31+.......+a_{n-1}+a_n$$ $$S=3+7+13+21+31+...+a_{n-2}+a_{n-1}+a_n$$$

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:

Time Complexity : O(1)

Auxiliary Space: O(1)

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