Program to find Nth term of series 9, 23, 45, 75, 113…

Given a number N, the task is to find the Nth term in the given series:

9, 23, 45, 75, 113, 159......

Examples:

Input: 4
Output: 113
Explanation:
For N = 4
Nth term = ( 2 * N + 3 )*( 2 * N + 3 ) - 2 * N
         = ( 2 * 4 + 3 )*( 2 * 4 + 3 ) - 2 * 4
         = 113

Input: 10
Output: 509

Approach:
The Nth term of the given series can be generalised as:



Nth term of the series : ( 2 * N + 3 )*( 2 * N + 3 ) - 2 * N

Below is the implementation of the above problem:

Program:

C++

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// CPP program to find N-th term of the series:
// 9, 23, 45, 75, 113...
  
#include <iostream>
using namespace std;
  
// calculate Nth term of series
int nthTerm(int N)
{
    return (2 * N + 3) * (2 * N + 3) - 2 * N;
}
  
// Driver Function
int main()
{
  
    // Get the value of N
    int N = 4;
  
    // Find the Nth term
    // and print it
    cout << nthTerm(N);
  
    return 0;
}

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Java

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// Java program to find 
// N-th term of the series: 
// 9, 23, 45, 75, 113... 
  
class GFG 
{
  
// calculate Nth term of series 
static int nthTerm(int N) 
    return (2 * N + 3) * 
           (2 * N + 3) - 2 * N; 
  
// Driver code
public static void main(String[] args)
{
      
    // Get the value of N 
    int N = 4
      
    // Find the Nth term 
    // and print it 
    System.out.println(nthTerm(N));
}
}
  
// This code is contributed by Bilal

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Python3

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# Python program to find 
# N-th term of the series: 
# 9, 23, 45, 75, 113... 
def nthTerm(N): 
      
    # calculate Nth term of series
    return ((2 * N + 3) * 
            (2 * N + 3) - 2 * N);
  
# Driver Code 
  
# Get the value of N 
n = 4
  
# Find the Nth term 
# and print it 
print(nthTerm(n)) 
  
# This code is contributed by Bilal

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C#

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// C# program to find 
// N-th term of the series: 
// 9, 23, 45, 75, 113... 
using System;
  
class GFG 
{
  
// calculate Nth term of series 
static int nthTerm(int N) 
    return (2 * N + 3) * 
           (2 * N + 3) - 2 * N; 
  
// Driver code
public static void Main()
{
      
    // Get the value of N 
    int N = 4; 
      
    // Find the Nth term 
    // and print it 
    Console.WriteLine(nthTerm(N));
}
}
  
// This code is contributed
// by Akanksha Rai(Abby_akku)

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PHP

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<?php
// PHP program to find 
// N-th term of the series:
// 9, 23, 45, 75, 113...
  
// calculate Nth term of series
function nthTerm($N)
{
    return (2 * $N + 3) * 
           (2 * $N + 3) - 2 * $N;
}
  
// Driver Code
  
// Get the value of N
$N = 4;
  
// Find the Nth term
// and print it
echo nthTerm($N);
  
// This code is contributed by Raj
?>

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Output:

113

Time Complexity: O(1)



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