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 [Tex] [/Tex]

Below is the implementation of the above approach as follows: 

C++

// 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;
}

// Main driver method
int main()
{
  // Declaration of number of terms
    long long int N = 10;

    // Getting the Nth term
    cout << getNthTerm(N);

    return 0;
}

Java

// 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));

}
}

Python3

# 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

C#

// 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

PHP

<?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
?>

Javascript

<script>

// javascript 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 * Math.pow(N, 2) - 3 * N + 2;
}

// driver code

    // declaration of number of terms
    let N = 10;

    // Get the Nth term
    document.write( getNthTerm(N));

// This code contributed by gauravrajput1

</script>

Output:

372

Time Complexity: O(logN) because it is using inbuilt pow function

Auxiliary Space: O(1) // As it is using constant variables