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# Program to find the Nth term of the series 3, 7, 13, 21, 31…..

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

3, 7, 13, 21, 31, …….

Examples:

Input: N = 4
Output: 21
Explanation:
Nth term = (pow(N, 2) + N + 1)
= (pow(4, 2) + 4 + 1)
= 21

Input: N = 11
Output: 133

Approach:

Subtracting these two equations we get

Therefore, the Nth Term of the given series is:

Below is the implementation of the above approach:

## C++

 // CPP program to find the Nth term of given series.#include #include using namespace std; // Function to calculate sumlong long int getNthTerm(long long int N){    // Return Nth term    return (pow(N, 2) + N + 1);} // driver codeint main(){    // declaration of number of terms    long long int N = 11;     // Get the Nth term    cout << getNthTerm(N);     return 0;}

## Java

 // Java code to find the Nth term of given series.import java.util.*; class solution{ // Function to calculate sumstatic long getNthTerm(long N){        // Return Nth term    return ((int)Math.pow(N, 2) + N + 1);} //Driver programpublic static void main(String arr[]){        // declaration of number of terms    long N = 11;     // Get the Nth term    System.out.println(getNthTerm(N)); }}//THis code is contributed by//Surendra_Gangwar

## Python3

 # Python3 Code to find the# Nth term of given series. # Function to calculate sumdef getNthTerm(N):         # Return Nth term    return (pow(N, 2) + N + 1) # driver codeif __name__=='__main__':     # declaration of number of terms    N = 11     # Get the Nth term    print(getNthTerm(N)) # This code is contributed by# Sanjit_Prasad

## C#

 // C# code to find the Nth// term of given series.using System; class GFG{ // Function to calculate sumstatic long getNthTerm(long N){     // Return Nth term    return ((int)Math.Pow(N, 2) + N + 1);} // Driver Codestatic public void Main (){         // declaration of number    // of terms    long N = 11;     // Get the Nth term    Console.Write(getNthTerm(N));}} // This code is contributed by Raj

## PHP

 

## Javascript

 

Output:

133

Time Complexity: O(1)
Space Complexity: O(1) since using constant variables

Method 2: We can also solve the problem by the formula [ (n+1)2-n  ].

## C++

 // CPP program to find the Nth term of given series.#include #include using namespace std; // Function to calculate sumlong long int getNthTerm(long long int N){    // Return Nth term    return (pow(N + 1, 2) - N);} // driver codeint main(){    // declaration of number of terms    long long int N = 11;     // Get the Nth term    cout << getNthTerm(N);     return 0;}

## Python3

 # Python program to find the Nth term of given series.import math # Function to calculate sumdef getNthTerm(N):    # Return Nth term    return int(math.pow(N + 1, 2) - N) # driver codeif __name__ == '__main__':    # declaration of number of terms    N = 11     # Get the Nth term    print(getNthTerm(N))

Output

133

Time Complexity: O(logN)
Space Complexity: O(1) since using constant variables

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