Find Nth number of the series 1, 6, 15, 28, 45, …..

• Last Updated : 28 Apr, 2021

Given the first two numbers of a series. The task is to find the Nth( N may be up to 10^18) number of that series.
Note: Every Element in the array is two less than the mean of the number preceding and succeeding of it. The answer can be very large so print answer under modulo 10^9+9.
Examples

Input: N = 3
Output: 15
(1 + 15)/2 - 2 = 6

Input: N = 4
Output: 28
(6 + 28)/2 - 2 = 15

Observation: According to the statement, the series formed will be 1, 6, 15, 28, 45….. So, the formula for Nth term will be:

2*n*n - n

C++

 // CPP program to find Nth term of the series#include using namespace std;#define mod 1000000009 // function to return nth term of the seriesint NthTerm(long long n){    long long x = (2 * n * n) % mod;    return (x - n + mod) % mod;} // Driver codeint main(){    long long N = 4;     // function call    cout << NthTerm(N);     return 0;}

Java

 // Java program to find N-th// term of the series: import java.util.*;import java.lang.*;import java.io.*; class GFG {     // function to return nth term of the series    static long NthTerm(long n)    {        long x = (2 * n * n) % 1000000009;        return (x - n + 1000000009) % 1000000009;    }     // Driver Code    public static void main(String args[])    {         // Taking  n as 6        long N = 4;         // Printing the nth term        System.out.println(NthTerm(N));    }}

Python

 # Python 3 program to find # N-th term of the series:     # Function for calculating # Nth term of series def NthTerm(N) :        # return nth term    x = (2 * N*N)% 1000000009    return ((x - N + 1000000009)% 1000000009)    # Driver code if __name__ == "__main__" :            N = 4       # Function Calling     print(NthTerm(N))

C#

 // C# program to find N-th// term of the series:using System; class GFG{ // function to return nth// term of the seriesstatic long NthTerm(long n){    long x = (2 * n * n) % 1000000009;    return (x - n + 1000000009) %                    1000000009;} // Driver Codepublic static void Main(){     // Taking n as 6    long N = 4;     // Printing the nth term    Console.WriteLine(NthTerm(N));}} // This code is contributed// by inder_verma



Javascript


Output:
28

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