Program to find Nth term of the series 3, 12, 29, 54, 87, …

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

3, 12, 29, 54, 87, ………….

Examples:



Input: N = 4
Output: 54
Explanation:
Nth term = 4 * pow(n, 2) - 3 * n + 2
         = 4 * pow(4, 2) - 3 * 4 + 2
         = 54

Input: N = 10
Output: 372

Approach:

The Nth Term of the given series is:

Nth term of the series T_n = 4 * n * n - 3 * n + 2

Below is the implementation of the above approach:

C++

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// CPP program to find N-th term of the series:
// 3, 12, 29, 54, 87, ...
  
#include <iostream>
#include <math.h>
using namespace std;
  
// calculate Nth term of series
int getNthTerm(long long int N)
{
    // Return Nth term
    return 4 * pow(N, 2) - 3 * N + 2;
}
  
// driver code
int main()
{
    // declaration of number of terms
    long long int N = 10;
  
    // Get the Nth term
    cout << getNthTerm(N);
  
    return 0;
}

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Java

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// Java program to find N-th term of the series:
// 3, 12, 29, 54, 87, ...
  
import java.util.*;
class solution
{
  
static long getNthTerm(long N)
{
    // Return Nth term
    return 4 *(long)Math.pow(N, 2) - 3 * N + 2;
}
  
//Driver code
public static void main(String arr[])
{
// declaration of number of terms
    long N = 10;
  
    // Get the Nth term
    System.out.println(getNthTerm(N));
  
}
}

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Python3

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# Python3 program to find N-th term of the series:
# 3, 12, 29, 54, 87, ...
  
# calculate Nth term of series
def getNthTerm(N):
  
    # Return Nth term
    return 4 * pow(N, 2) - 3 * N + 2
  
# driver code
if __name__=='__main__':
      
    # declaration of number of terms
    N = 10
  
    # Get the Nth term
    print(getNthTerm(N))
  
# This code is contributed by
# Sanjit_Prasad

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C#

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// C# program to find 
// N-th term of the series:
// 3, 12, 29, 54, 87, ...
using System;
  
class GFG
{
static long getNthTerm(long N)
{
    // Return Nth term
    return 4 * (long)Math.Pow(N, 2) - 
                         3 * N + 2;
}
  
// Driver code
static public void Main ()
  
    // declaration of number
    // of terms
    long N = 10;
      
    // Get the Nth term
    Console.Write(getNthTerm(N));
}
}
  
// This code is contributed by Raj

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PHP

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<?php
// PHP program to find
// N-th term of the series:
// 3, 12, 29, 54, 87, ...
  
// calculate Nth term of series
function getNthTerm($N)
{
    // Return Nth term
    return 4 * pow($N, 2) - 
           3 * $N + 2;
}
  
// Driver code
  
// declaration of number of terms
$N = 10;
  
// Get the Nth term
echo getNthTerm($N);
  
// This code is contributed 
// by inder_verma
?>

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Output:

372

Time Complexity: O(1)



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