Find n-th term in the series 7, 15, 32, …

Given a series 7, 15, 32, …… Find the nth term of this series.

Examples :

Input : 5
Output : 138

Input : 7
Output : 568 

Approach: By seeing the pattern of the series we can easily identify that it is a mixed series. 
S = 7, 15, 32….. 
Each element in the series is multiplied by 2 and then incremented one more than the previous. 
S = 7, 15 (2 * 7 + 1), 32 (2 * 15 + 2)…….
By using iteration we can easily find nth term of the series.

Below is the implementation of the above approach :  

C++

// CPP program to find nth term
#include <bits/stdc++.h>
using namespace std;

// utility function
int findTerm(int n)
{
    if (n == 1)
        return n;

    else {

        // since first element of the
        // series is 7, we initialise
        // a variable with 7
        int term = 7;

        // Using iteration to find nth
        // term
        for (int i = 2; i <= n; i++)
            term = term * 2 + (i - 1);

        return term;
    }
}

// driver function
int main()
{
    int n = 5;
    cout << findTerm(n);
    return 0;
}

Java

// Java program to find nth term
import java.lang.*;

class GFG {

// utility function
static int findTerm(int n)
{
    if (n == 1)
    return n;

    else {

    // since first element of the
    // series is 7, we initialise
    // a variable with 7
    int term = 7;

    // Using iteration to find nth
    // term
    for (int i = 2; i <= n; i++)
        term = term * 2 + (i - 1);

    return term;
    }
}

// Driver code
public static void main(String[] args)
{
    int n = 5;
    System.out.print(findTerm(n));
}
}

// This code is contributed by Anant Agarwal.

Python3

# Python3 program to find nth term

# utility function
def findTerm(n) :

    if n == 1 :
        return n
    else :

        # since first element of the
        # series is 7, we initialise
        # a variable with 7
        term = 7

        # Using iteration to find nth
        # term
        for i in range(2, n + 1) :
            term = term * 2 + (i - 1);

    return term;

# driver function
print (findTerm(5))

# This code is contributed by Saloni Gupta

C#

// C# program to find nth term
using System;

class GFG {

    // utility function
    static int findTerm(int n)
    {
        if (n == 1)
            return n;

        else {

            // since first element of the
            // series is 7, we initialise
            // a variable with 7
            int term = 7;

            // Using iteration to find nth
            // term
            for (int i = 2; i <= n; i++)
                term = term * 2 + (i - 1);

            return term;
        }
    }

    // Driver code
    public static void Main()
    {
        int n = 5;
        Console.WriteLine(findTerm(n));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP program to find nth term

// utility function
function findTerm($n)
{
    if ($n == 1)
        return $n;

    else
    {

        // since first element of the
        // series is 7, we initialise
        // a variable with 7
        $term = 7;

        // Using iteration to find nth
        // term
        for ($i = 2; $i <= $n; $i++)
            $term = $term * 2 + ($i - 1);

        return $term;
    }
}

// Driver Code
$n = 5;
echo(findTerm($n));

// This code is contributed by Ajit.
?>

Javascript

<script>
// Javascript program to find nth term

// utility function
function findTerm(n)
{
    if (n == 1)
        return n;

    else
    {

        // since first element of the
        // series is 7, we initialise
        // a variable with 7
        let term = 7;

        // Using iteration to find nth
        // term
        for (let i = 2; i <= n; i++)
            term = term * 2 + (i - 1);

        return term;
    }
}

// Driver Code
let n = 5;
document.write(findTerm(n));

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

Output

138

Time Complexity: O(n) since for loop will run for n times in worst case
Auxiliary Space: O(1)