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Find the sum of series 3, 7, 13, 21, 31….
  • Difficulty Level : Medium
  • Last Updated : 22 Mar, 2021

Given a number N. The task is to find the sum of below series upto nth 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: 
 

image

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)
 

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