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Find Nth term of the series 2, 3, 10, 15, 26….

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  • Last Updated : 20 Aug, 2022
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Given a number N, the task is to find the Nth term in series 2, 3, 10, 15, 26….
Example: 
 

Input: N = 2
Output: 3
2nd term = (2*2)-1
         = 3

Input: N = 5
Output: 26
5th term = (5*5)+1
         = 26

 

Approach:
 

  • Nth number of the series is obtained by 
    1. Squaring the number itself.
    2. If the number is odd, add 1 to the squared number. And, subtract 1 if the number is even
  • Since the starting number of the series is 2
    1st term = 2 
    2nd term = (2 * 2) – 1 = 3 
    3rd term = (3 * 3) + 1 = 10 
    4th term = (4 * 4) – 1 = 15 
    5th term = (5 * 5) + 1 = 26 
    and so on…. 
     
  • In general, Nth number is obtained by formula: 
     

  •  

Below is the implementation of the above approach: 
 

C++




// C++ program to find Nth term
// of the series 2, 3, 10, 15, 26....
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find Nth term
int nthTerm(int N)
{
    int nth = 0;
 
    // Nth term
    if (N % 2 == 1)
        nth = (N * N) + 1;
    else
        nth = (N * N) - 1;
 
    return nth;
}
 
// Driver Method
int main()
{
    int N = 5;
 
    cout << nthTerm(N) << endl;
 
    return 0;
}

Java




// Java program to find Nth term
// of the series 2, 3, 10, 15, 26....
class GFG
{
 
// Function to find Nth term
static int nthTerm(int N)
{
    int nth = 0;
 
    // Nth term
    if (N % 2 == 1)
        nth = (N * N) + 1;
    else
        nth = (N * N) - 1;
 
    return nth;
}
 
// Driver code
public static void main(String[] args)
{
    int N = 5;
 
    System.out.print(nthTerm(N) +"\n");
 
}
}
 
// This code is contributed by Rajput-Ji

Python3




# Python3 program to find Nth term
# of the series 2, 3, 10, 15, 26....
 
# Function to find Nth term
def nthTerm(N) :
    nth = 0;
 
    # Nth term
    if (N % 2 == 1) :
        nth = (N * N) + 1;
    else :
        nth = (N * N) - 1;
 
    return nth;
 
# Driver Method
if __name__ == "__main__" :
    N = 5;
    print(nthTerm(N)) ;
 
# This code is contributed by AnkitRai01

C#




// C# program to find Nth term
// of the series 2, 3, 10, 15, 26....
using System;
 
class GFG
{
 
// Function to find Nth term
static int nthTerm(int N)
{
    int nth = 0;
 
    // Nth term
    if (N % 2 == 1)
        nth = (N * N) + 1;
    else
        nth = (N * N) - 1;
 
    return nth;
}
 
// Driver code
public static void Main(String[] args)
{
    int N = 5;
 
    Console.Write(nthTerm(N) +"\n");
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
    // Javascript program to find Nth term
    // of the series 2, 3, 10, 15, 26....
     
    // Function to find Nth term
    function nthTerm(N)
    {
        let nth = 0;
 
        // Nth term 
        if (N % 2 == 1)
            nth = (N * N) + 1;
        else
            nth = (N * N) - 1;
 
        return nth;
    }
     
    let N = 5;
    document.write(nthTerm(N));
 
// This code is contributed by divyeshrabadiya07.
</script>

Output: 

26

 

Time Complexity: O(1) since no loop is used the algorithm takes up constant time to perform the operations

Auxiliary Space: O(1) since no extra array is used so the space taken by the algorithm is constant


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