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

• Difficulty Level : Medium
• Last Updated : 19 Jul, 2022

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:

Sum of first n terms of this series:

Therefore, Sum of first n terms of this series:
Below is the implementation of the above approach:

C++

 // CPP program to find sum // upto N-th term of the series: // 23, 45, 75, 113...   #include  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; }

Java

 // 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));   } }

Python3

 # 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

C#

 // 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

PHP

 

Javascript

 

Output:

256

Time Complexity: O(1)

Auxiliary Space: O(1) since using constant variables

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