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 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++

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// 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;
}

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Java

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// 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

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Python 3

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# 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)))

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C#

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// 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.

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PHP

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<?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
?>

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Output:

5875

Time Complexity : O(1)



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