Program to find N-th term of series a, b, b, c, c, c…in C++

In this problem, we are given a number N. Our task is to create a Program to find N-th term of series a, b, b, c, c, c…in C++.

Problem Description

To find the Nth term of the series −

a, b, b, c, c, c, d, d, d, d,....Nterms 

We need to find the general term of the series.

Let’s take an example to understand the problem,

Input

N = 7

Output

d

Solution Approach

To find the general term of the series, we need to closely observe the series. The series has 1 a, 2 b’s, 3 c’s, 4 d’s,... This seems to be an AP. And the Nth term is the sum of AP which a and d both 1.

Sum of AP = Nth Term = (n/2)(a+(n-1)d).

The n specifies which character is the Nth term.

Now, lets derive the value of n,

Nth Term = (n/2)*(1 + (n-1)*1)
   (n/2)*(1 + n - 1)
   (n/2)*n

$\sqrt{2\square^2}$

Example

 Live Demo

#include <iostream>
#include <math.h>
using namespace std;
char findNTerm(int N) {
   int n = sqrt(2*N);
   return ((char)('a' + n));
}
int main() {
   int N = 54;
   cout<<N<<"th term of the series is "<<findNTerm(N);
   return 0;
}

Output

54th term of the series is k