Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
C++ Programe to find n-th term in series 1 2 2 3 3 3 4
In this problem, we are given an integer N. The task is to find n-th term in series 1 2 2 3 3 3 4….
Let’s take an example to understand the problem,
Input
N = 6
Output
3
Explanation
The series upto nth term is 1, 2, 2, 3, 3, 3, ...
Solution Approach
A simple approach to solve the problem is by using a nested loop. The outer for loop is from 1 to n. And the inner loop is from 1 to i (iterator of outer loop). For each iteration in the inner loop, count the number of elements of the series and return the value of i when count is equal to n.
A more efficient approach to solve the problem is using pattern positions. The elements of the sequence is with their positions in the series are −
Element 1: position 1 Element 2: position 2, 3 Element 3: position 4, 5, 6 Element 4: position 7, 8, 9, 10
For these values, we can create a series using the last position of element in the series which is,
1, 3, 6, 10, 15, 21, 28, ….
x appears in term, 1 + 2 + 3 + … + (x-2) + (x-1)...
This can be generalised as n = x*(x-1)/2
2n = x2 - x => x2 - x - 2n = 0
Solve the equation using formula for solution of quadratic equation,
$$x=1/2*(1+\sqrt{1+8*n)}$$
Program to illustrate the working of our solution,
Example
#include <bits/stdc++.h>
using namespace std;
int findNthTerm(int n) {
int x = (((1) + (double)sqrt(1 + (8 * n))) / 2);
return x;
}
int main(){
int n = 12;
cout<<"The series is 1, 2, 2, 3, 3, 3, 4, 4, ...\n";
cout<<n<<"th term of the series is "<<findNthTerm(n);
return 0;
}Output
The series is 1, 2, 2, 3, 3, 3, 4, 4, ... 12th term of the series is 5
251 Views
