1 3 7 13 21

Plan to find the Nth term of the series 3, vii, 13, 21, 31…..

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Given a number Due north, the task is to notice the Nth term of this serial:

3, seven, thirteen, 21, 31, …….

Examples:

            Input:            N = iv            Output:            21            Explanation:            Nth term = (pow(N, 2) + N + i)          = (pow(4, 2) + 4 + 1)          = 21            Input:            Northward = 11            Output:            133

Approach:
$Sum = 0+3+7+13+21+31+........+a_{n-1} + a_n\\ Sum = 3+7+13+21+31+...+a_{n-2}+a_{n-1}+a_n$
Subtracting these two equations we get
$0=3+\left \{\frac{n-1}{2}\right \}[2*4 + (n-2)*2]-a_n\\ =3+\left \{\frac{n-1}{2}\right \}[8 + 2n-4]-a_n\\ =3+\left \{\frac{n-1}{2}\right \}[2n+4]-a_n\\ a_n=3+(n-1)(n+2)\\ a_n=n^2+n+1$
Therefore, the Nth Term of the given series is:

Below is the implementation of the to a higher place approach:

C++

                #include <iostream>              
                #include <math.h>              
                using                namespace                std;              
                long                long                int                getNthTerm(                long                long                int                North)              
                {              
                                return                (                pow                (N, 2) + N + 1);              
                }              
                int                main()              
                {              
                                long                long                int                N = 11;              
                                cout << getNthTerm(North);              
                                return                0;              
                }              

Java

                import                java.util.*;              
                class                solution              
                {              
                static                long                getNthTerm(                long                N)              
                {              
                                return                ((                int                )Math.pow(N,                                two                ) + N +                                1                );              
                }              
                public                static                void                primary(String arr[])              
                {              
                                long                North =                                11                ;              
                                System.out.println(getNthTerm(N));              
                }              
                }              

Python3

                def                getNthTerm(N):              
                                return                (                pw                (N,                                2                )                                +                N                                +                i                )              
                if                __name__                =                =                '__main__'                :              
                                Due north                                =                eleven              
                                print                (getNthTerm(N))              

C#

                using                System;              
                class                GFG              
                {              
                static                long                getNthTerm(                long                N)              
                {              
                                return                ((                int                )Math.Pow(N, ii) + N + 1);              
                }              
                static                public                void                Main ()              
                {              
                                long                N = 11;              
                                Console.Write(getNthTerm(North));              
                }              
                }              

PHP

                <?php              
                function                getNthTerm(                $N                )              
                {              
                                render                (pow(                $Northward                , 2) +                                $Due north                + 1);              
                }              
                $Due north                = eleven;              
                echo                getNthTerm(                $North                );              
                ?>              

Javascript

                <script>              
                function                getNthTerm(North)              
                {              
                                return                (Math.pow(North, two) + Due north + 1);              
                }              
                                let N = 11;              
                                document.write(getNthTerm(N));              
                </script>              