Find N-th term of series 2, 8, 18, 32, 50…

Given the series 2, 8, 18, 32, 50…, find the Nth term of the series.

Examples:

Input: N = 1
Output: 2

Input: N = 3
Output: 18

Input: N = 5
Output: 50

Approach:

For finding the nth term we need to find the relation between n and each term.

1st term = 2 =  2*(1²) // 2*first perfect square

2nd term = 8 = 2*(2²) // 2*second perfect square

3rd term = 18 = 2*(3²) //  2*third perfect square

4th term = 32 = 2*(4²) //  2*fourth perfect square

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Nth term = 2*(Nth perfect square)

Formula-

T_N = 2 * N ^ 2

Illustration-

Input: N = 5
Output: 50
Explanation-
T_N = 2 * N ^ 2
     = 2* 5 ^ 2
     = 2 * 25
     = 50

Below is the C++ program to implement the above approach-

C++

// C++ program to implement
// the above approach
#include <iostream>
using namespace std;

// Find n-th term of series
// 2, 8, 18, 32, 50...
int nthTerm(int N)
{

    // Nth perfect square is N * N
    int Nthperfectsquare = N * N;

    return 2 * Nthperfectsquare;
}
// Driver code
int main()
{
    int N = 5;

    cout << nthTerm(N) << endl;
    return 0;
}

Java

// Java code for the above approach

import java.io.*;

class GFG {

// Find n-th term of series
// 2, 8, 18, 32, 50...
static int nthTerm(int N)
{

    // Nth perfect square is N * N
    int Nthperfectsquare = N * N;

    return 2 * Nthperfectsquare;
}
// Driver code
    public static void main (String[] args) {

       int N = 5;

        System.out.println(nthTerm(N));
    }
}
// This code is contributed by Potta Lokesh

Python

# Python program to implement
# the above approach

# Find n-th term of series
# 2, 8, 18, 32, 50...
def nthTerm(N):

    # Nth perfect square is N * N
    Nthperfectsquare = N * N

    return 2 * Nthperfectsquare

# Driver Code
if __name__ == "__main__":

    N = 5

    print(nthTerm(N))

# This code is contributed by Samim Hossain Mondal.

C#

using System;

public class GFG{

// Find n-th term of series
// 2, 8, 18, 32, 50...
static int nthTerm(int N)
{

    // Nth perfect square is N * N
    int Nthperfectsquare = N * N;

    return 2 * Nthperfectsquare;
}

// Driver code
static public void Main (){

    int N = 5;
    Console.Write(nthTerm(N));
}
}

// This code is contributed by hrithikgarg03188

Javascript

<script>
// Javascript program to implement
// the above approach

// Find n-th term of series
// 2, 8, 18, 32, 50...
function nthTerm(N)
{

    // Nth perfect square is N * N
    let Nthperfectsquare = N * N;

    return 2 * Nthperfectsquare;
}

// Driver code
let N = 5;

document.write(nthTerm(N))

// This code is contributed by gfgking.
</script>

Output:

50

Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.