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Find the Nth term of the series 1 + 2 + 6 + 15 + 31 + 56 + …
• Difficulty Level : Easy
• Last Updated : 12 Apr, 2021

Given an integer . The task is to write a program to find the N-th term of the given series:

1 + 2 + 6 + 15 + 31 + 56 + ...

Examples

Input : N = 8
Output : 141

Input : N = 20
Output : 2471

Approach:
The given series is:

1, 2, 6, 15, 31, 56, 92, 141, ...

First consecutive difference

1 4 9 16 25 36 49 .......

Second consecutive difference

3 5 7 9 11 13......

As the second consecutive difference is in AP, the nth term (tn) of the series is of the form,
A(n – 1)(n – 2)(n – 3) + B(n – 1)(n – 2) + C(n – 1) + D
So, tn = A(n – 1)(n – 2)(n – 3) + B(n – 1)(n – 2) + C(n – 1) + D
Now,
t1 = D = 1
t2 = C (2 – 1) + D = 2
t3 = 2B + 2C + D = 6
t4 = CA + 6B + 3C + D = 15
On solving the above four equations we get => A = 1/3, B = 3/2, C = 1, D = 1. On substituting these values tn and after simplifying we get,

Below is the implementation of above approach:

## C++

 // C++ program to find Nth// term of the series:// 1 + 2 + 6 + 15 + 31 + 56 + ...#include#includeusing namespace std; // calculate Nth term of given seriesint Nth_Term(int n){    return (2 * pow(n, 3) - 3 *                pow(n, 2) + n + 6) / 6;} // Driver codeint main(){    int N = 8;    cout << Nth_Term(N);}

## Java

 // Java program to find Nth// term of the series:// 1 + 2 + 6 + 15 + 31 + 56 + ...import java.util.*;import java.lang.*; class GFG{// calculate Nth term of given seriesstatic double Nth_Term(int n){    return (2 * Math.pow(n, 3) - 3 *                Math.pow(n, 2) + n + 6) / 6;} // Driver codestatic public void main (String args[]){    int N = 8;    System.out.println(Nth_Term(N));}} // This code is contributed// by Akanksha Rai

## Python3

 # Python program to find Nth term of the series:# 1 + 2 + 6 + 15 + 31 + 56 + ... # calculate Nth term of given seriesdef Nth_Term(n):    return (2 * pow(n, 3) - 3 * pow(n, 2) + n + 6) // 6 # Driver codeN = 8print(Nth_Term(N))

## C#

 // C# program to find Nth// term of the series:// 1 + 2 + 6 + 15 + 31 + 56 + ...using System; class GFG{// calculate Nth term of given seriesstatic double Nth_Term(int n){    return (2 * Math.Pow(n, 3) - 3 *                Math.Pow(n, 2) + n + 6) / 6;} // Driver codestatic public void Main (){    int N = 8;    Console.WriteLine(Nth_Term(N));}} // This code is contributed// by Sach_Code

## PHP

 

## Javascript

 
Output:
141

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