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

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  • Difficulty Level : Medium
  • Last Updated : 10 Aug, 2022

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[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


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