Program to find the Nth term of the series 3, 20, 63, 144, 230, ……

Given a series and a number N. The task is to find the Nth term of the given series:

3, 20, 63, 144, 230 …..

Examples:

Input: N = 4
Output: 144
When n = 4
nth term = 2 ( n * n * n ) + n * n
         = 2 ( 4 * 4 * 4 ) + 4 * 4
         = 144

Input: N = 10
Output: 2100


Approach: We can find the general term (Tn) of the given series.
  series\: can\: be\: written\: in\: the\: following\: way\: also:\\ (3 * 1^2), (5 * 2^2), (7 * 3^2), (9 * 4^2), .......up t n terms\\ Tn = (\:General\; term\; of \;series\; 3, 5, 7, 9 ....\;)\; X\; (\;General\; term\; of\; series\; 1^2, 2^2, 3^2, 4^2 ....\;)\\ Tn = (3 + (n-1) * 2) X ( n^2 )\\ Tn = 2*n^3 + n^2

Below is the required implementation:

C++

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// CPP program to find N-th term of the series:
// 3, 20, 63, 144, 230 .....
#include <iostream>
#include <math.h>
using namespace std;
  
// calculate Nth term of series
int nthTerm(int n)
{
    return 2 * pow(n, 3) + pow(n, 2);
}
  
// Driver code
int main()
{
    int N = 3;
  
    cout << nthTerm(N);
  
    return 0;
}

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Java

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// Java program to find N-th term of the series:
// 3, 20, 63, 144, 230 .....
import java.util.*;
  
class solution
{
  
// calculate Nth term of series
static int nthTerm(int n)
{
    //return final sum
    return 2 *(int)Math.pow(n, 3) + (int)Math.pow(n, 2);
}
  
// Driver code
public static void main(String arr[])
{
    int N = 3;
  
System.out.println(nthTerm(N));
  
}
  
}
//This code is contributed by Surendra_Gangwar

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Python 3

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# Python program to find
# N-th term of the series: 
# 3, 20, 63, 144, 230 .....
  
# calculate Nth term of series 
def nthTerm(n) :
  
    return 2 * pow(n, 3) + pow(n, 2)
  
# Driver code
if __name__ == "__main__" :
  
    N = 3
    print(nthTerm(N))
  
# This code is contributed 
# by ANKITRAI1

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C#

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// C# program to find N-th term of the series:
// 3, 20, 63, 144, 230 .....
using System;
  
class solution
{
  
// calculate Nth term of series
static int nthTerm(int n)
{
    //return final sum
    return 2 *(int)Math.Pow(n, 3) + (int)Math.Pow(n, 2);
}
  
// Driver code
public static void Main()
{
    int N = 3;
  
Console.WriteLine(nthTerm(N));
  
}
  
}
//This code is contributed by  Shashank

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PHP

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<?php
// PHP program to find 
// N-th term of the series:
// 3, 20, 63, 144, 230 .....
  
// calculate Nth term of series
function nthTerm($n)
{
    return 2 * pow($n, 3) + 
               pow($n, 2);
}
  
// Driver code
$N = 3;
echo nthTerm($N);
  
//This code is contributed by Shashank
?>

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Output:

63

Time Complexity: O(1)



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