Program to find the sum of the series 23+ 45+ 75+….. upto N terms

Given a number N, the task is to find the Nth term of the below series:

23 + 45 + 75 + 113 + 159 +…… upto N terms

Examples:

Input: N = 4
Output: 256
Explanation:
Nth term = (2 * N * (N + 1) * (4 * N + 17) + 54 * N) / 6
         = (2 * 4 * (4 + 1) * (4 * 4 + 17) + 54 * 4) / 6
         = 256

Input: N = 10
Output: 2180

Approach:

The Nth term of the given series can be generalized as:
 T_n = ( 2 * n + 3 )^2 - 2 * n\\  T_n = 4 * n^2+ 10*n+9

Sum of first n terms of this series:
$S_n=4\sum_{i=1}^n n^2+10\sum_{i=1}^n n +9\sum_{i=1}^n 1\\\\  S_n=4\frac{n(n+1)(2n+1)}{6}+30\frac{n(n+1)}{2} +9n\\\\ $

Therefore, Sum of first n terms of this series: S_n=\frac{2n(n+1)(4n+17)+54n}{6}

Below is the implementation of the above approach:

C++

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// CPP program to find sum
// upto N-th term of the series:
// 23, 45, 75, 113...
  
#include <iostream>
using namespace std;
  
// calculate Nth term of series
int findSum(int N)
{
    return (2 * N * (N + 1) * (4 * N + 17) + 54 * N) / 6;
}
  
// Driver Function
int main()
{
  
    // Get the value of N
    int N = 4;
  
    // Get the sum of the series
    cout << findSum(N) << endl;
  
    return 0;
}

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Java

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// Java program to find sum
// upto N-th term of the series:
// 23, 45, 75, 113...
import java.util.*;
  
class solution 
{
      
static int findSum(int N)
{
    //return the final sum
    return (2 * N * (N + 1) * (4 * N + 17) + 54 * N) / 6;
}
  
//Driver program
public static void main(String arr[])
{
// Get the value of N
    int N = 4;
  
// Get the sum of the series
 System.out.println(findSum(N));
  
}
}

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Python3

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# Python3 program to find sum
# upto N-th term of the series:
# 23, 45, 75, 113...
  
# calculate Nth term of series 
def findSum(N):
      
    return (2 * N * (N + 1) * (4 * N + 17) + 54 * N) / 6
      
#Driver Function
if __name__=='__main__':
#Get the value of N
    N = 4
  
#Get the sum of the series
    print(findSum(N))
  
#this code is contributed by Shashank_Sharma

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C#

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// C# program to find sum 
// upto N-th term of the series: 
// 23, 45, 75, 113... 
using System; 
  
class GFG 
      
static int findSum(int N) 
    //return the final sum 
    return (2 * N * (N + 1) * 
           (4 * N + 17) + 54 * N) / 6; 
  
// Driver Code 
static void Main() 
    // Get the value of N 
    int N = 4; 
      
    // Get the sum of the series 
    Console.Write(findSum(N)); 
  
// This code is contributed by Raj

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PHP

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<?php
// PHP program to find sum
// upto N-th term of the series:
// 23, 45, 75, 113...
  
// calculate Nth term of series
function findSum($N)
{
    return (2 * $N * ($N + 1) * 
           (4 * $N + 17) + 54 * $N) / 6;
}
  
// Driver Code
  
// Get the value of N
$N = 4;
  
// Get the sum of the series
echo findSum($N);
  
// This code is contributed 
// by anuj_67
?>

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Output:

256

Time Complexity: O(1)



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