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<iostream>#include<math.h>using 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 series static double Nth_Term(int n) { return (2 * Math.pow(n, 3) - 3 * Math.pow(n, 2) + n + 6) / 6; } // Driver code static 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 series static double Nth_Term(int n) { return (2 * Math.Pow(n, 3) - 3 * Math.Pow(n, 2) + n + 6) / 6; } // Driver code static public void Main (){ int N = 8; Console.WriteLine(Nth_Term(N)); }}// This code is contributed// by Sach_Code |
PHP
<?php// PHP program to find Nth // term of the series:// 1 + 2 + 6 + 15 + 31 + 56 + ..// calculate Nth term of given seriesfunction Nth_Term($n){ return (2 * pow($n, 3) - 3 * pow($n, 2) + $n + 6) / 6;}// Driver code$N = 8;echo Nth_Term($N);// This code is contributed by // Shashank_Sharma?> |
Javascript
<script>// js program to find Nth// term of the series:// 1 + 2 + 6 + 15 + 31 + 56 + ..// calculate Nth term of given seriesfunction Nth_Term(n){ return (2 * Math.pow(n, 3) - 3 * Math.pow(n, 2) + n + 6) / 6;}// Driver codelet N = 8;document.write(Nth_Term(N));// This code is contributed // by pulamolu mohan pavan cse</script> |
141
Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.
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